Mirror reversal VS Rotation: Comparing motor adaptation and de novo learning
Raphael Gastrock
Overview
This document discusses results for the tablet and online experiments. We also provide a more in depth analysis of the date here, and show additional figures and statistics.
Set up the R enviornment
We have written code that pre-processes the data, plots figures, and runs statistical tests. Import the sources below:
source('ana/shared.R')
#tablet experiment scripts
source('ana/ordereffects.R')
source('ana/learningRates.R')
source('ana/exponentialandstepModel.R')
source('ana/individualDataCheck.R')
source('ana/rae.R')
source('ana/RTandMT.R')
source('ana/pathlength.R')
#online experiment scripts
source('ana/controlmir.R')
source('ana/controlmirgen.R')
source('ana/su&fa2020online.R')
source('ana/qualtricsdata.R')
source('ana/mironline_fa2020.R')
source('ana/mirgeneralization_fa2020.R')Study 1: Tablet experiment results
For the tablet experiment, half of the participants (N = 16) were simply told to compensate for the cursor moving differently during perturbed reaches, and the other half (N = 16) were instructed about the nature of each perturbation and was given a strategy to counter for it. We focus on the non-instructed participants for most of the analyses, as we only wanted to observe the effects of instructions on initial learning in each perturbation for the instructed participants.
Order Effects
Given that we implemented a within-subjects design for the tablet experiment, we first test whether learning one perturbation has an effect on learning the other. We also test for any effects in learning, depending on which axis each perturbation was experienced and the target locations relative to the perturbation axis.
Perturbation order
Rotation
For perturbation order, we expect that learning in each perturbation should not affect the other, regardless of which perturbation the participant experienced first.
plotNIROTOrderEffects()
For non-instructed participants, the percentage of compensation did not differ regardless of whether the rotation perturbation was experienced before or after mirror reversed perturbed reaches.
To quantify these comparisons between conditions better, we fit an exponential decay function that allowed us to measure learning rates and learning asymptotes. For perturbation order, we fit the exponential function to participants that either experienced the rotation before or after mirror reversed reaches.
plotROTOrderEffectsModel(group='noninstructed')
We then conducted t-tests to compare the learning rates and asymptotes between the two order conditions. Both frequentist and Bayesian tests are reported below.
getLambdaOrderEffectsTTest(perturbation='ROT')## Frequentist t-test (perturbation: ROT, condition: first vs. second):
##
## Welch Two Sample t-test
##
## data: subdat1 and subdat2
## t = -0.61244, df = 9.6387, p-value = 0.5544
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -0.1935460 0.1104204
## sample estimates:
## mean of x mean of y
## 0.1137463 0.1553091
##
## Bayesian t-test (perturbation: ROT, condition: first vs. second):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.4855399 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZSgetAsymptoteOrderEffectsTTest(perturbation='ROT')## Frequentist t-test (perturbation: ROT, condition: first vs. second):
##
## Welch Two Sample t-test
##
## data: subdat1 and subdat2
## t = -0.10034, df = 13.759, p-value = 0.9215
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -14.73630 13.42118
## sample estimates:
## mean of x mean of y
## 81.30748 81.96503
##
## Bayesian t-test (perturbation: ROT, condition: first vs. second):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.4290593 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZSThe tests confirmed that learning rates and learning asymptote did not differ regardless of whether the rotation was experienced before or after the other perturbation.
Mirror reversal
plotNIMIROrderEffects()
For the mirror reversed perturbed reaches, we also do not find differences depending on the order that they experienced the perturbation. However, note that the percentages of compensation have larger variability compared to those in the rotation perturbation.
We fit the same exponential decay function to both conditions and conducted t-tests to compare learning rates and asymptotes between perturbation order conditions.
plotMIROrderEffectsModel(groups='noninstructed')
We did not find any differences in learning rates and asymptotes between the mirror perturbation order conditions.
getLambdaOrderEffectsTTest(perturbation='MIR')## Frequentist t-test (perturbation: MIR, condition: first vs. second):
##
## Welch Two Sample t-test
##
## data: subdat1 and subdat2
## t = 1.0222, df = 8.0209, p-value = 0.3365
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -0.1615243 0.4189405
## sample estimates:
## mean of x mean of y
## 0.2549276 0.1262195
##
## Bayesian t-test (perturbation: MIR, condition: first vs. second):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.6055607 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZSgetAsymptoteOrderEffectsTTest(perturbation='MIR')## Frequentist t-test (perturbation: MIR, condition: first vs. second):
##
## Welch Two Sample t-test
##
## data: subdat1 and subdat2
## t = -1.436, df = 7.6622, p-value = 0.1905
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -221.17018 52.22542
## sample estimates:
## mean of x mean of y
## 108.1419 192.6143
##
## Bayesian t-test (perturbation: MIR, condition: first vs. second):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.835469 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZSModel comparisons
Since the mirror reversal data had more variability, we wanted to investigate whether different functions will fit the data better. For some participants, compensation seemed to immediately become better after a few trials. That is, it seemed like they figured things out after a certain trial, and suddenly started to perform better. The nature of such a performance resembled a logistic or step function. Therefore, in addition to the exponential decay function, we also fit both step and logistic functions to the rotation and mirror reversed data for each participant.
For the exponential decay function we get two parameters: lambda for the learning rate, and N0 for the asymptote. For the step function, instead of a learning rate, we get a step parameter to indicate where the change occurs. We also get an asymptote parameter. For the logistic function we get three parameters: x0 (the steepest part of the logistic function), k (the inverse of the steepness of the logistic function), and L (the scale of the function, which starts at 0 (at -infinity) and reaches L at infinity).
After fitting each function to each participant’s data, we also calculate mean squared errors (MSE) between each function and the data. The parameters and MSEs for the rotation perturbation are shown below. Each row will correspond to one participant.
read.csv('data/pilot/ROT_noninstructed_MSE_ordereffects.csv')## step asymptote mse_step lambda N0 mse_expl x0
## 1 12 72.98683 785.9078 0.05839083 81.57260 676.9233 12.552785
## 2 4 81.04288 456.9556 0.09788714 88.71477 252.5075 7.983897
## 3 12 60.44318 653.8266 0.09629438 62.55975 612.8795 10.666315
## 4 4 94.78372 361.9691 0.29441731 96.06407 310.4976 1.637205
## 5 4 70.74633 539.9778 0.11071178 76.33250 411.5146 5.026782
## 6 12 62.28616 881.3983 0.04072276 77.20361 671.5597 18.329900
## 7 12 101.79969 1774.4218 0.12128606 102.46256 1784.0515 10.396347
## 8 4 59.19791 483.4178 0.09026025 65.54994 354.8889 8.010550
## 9 4 71.36746 532.5357 0.04565858 89.73700 261.1401 16.116850
## 10 12 82.19301 614.3897 0.12774811 82.17503 652.5935 10.367659
## 11 12 83.50160 1034.1659 0.11175950 85.60478 897.5420 7.340905
## 12 20 85.93379 1221.9673 0.06040709 89.14594 1259.6360 17.073033
## 13 28 88.40681 2441.6112 0.04275045 92.69678 2558.5557 25.984972
## 14 4 56.09660 753.4171 0.57317597 56.14206 722.7989 -14.448589
## 15 4 69.99917 1784.2213 0.18681641 72.06938 1774.2605 7.971561
## 16 4 80.81635 534.7195 0.09415692 88.14930 429.3196 5.970294
## k L mse_log order
## 1 0.10750730 79.21128 693.2220 1
## 2 0.16637575 87.97088 242.8113 1
## 3 0.25203216 62.23388 596.3819 1
## 4 0.29018463 96.37510 274.6943 1
## 5 0.09724501 77.86428 385.5587 1
## 6 0.06693870 75.75177 653.3326 1
## 7 58.86733376 101.89029 1642.3959 1
## 8 0.10697776 66.13637 343.7633 1
## 9 0.05376664 92.27454 215.8416 2
## 10 2.41995703 82.10854 572.3963 2
## 11 0.19361682 85.30689 858.8186 2
## 12 23.39125037 85.70143 1088.3329 2
## 13 57.73534821 87.87973 2378.1958 2
## 14 0.07471177 56.46177 752.7031 2
## 15 50.91074901 71.76103 1791.1425 2
## 16 0.07429702 91.33297 408.3944 2The parameters and MSEs for the mirror reversed perturbation are shown below:
read.csv('data/pilot/MIR_noninstructed_MSE_ordereffects.csv')## step asymptote mse_step lambda N0 mse_expl x0
## 1 12 70.67695 10038.468 0.091272261 70.34986 10366.833 8.436232
## 2 4 86.00006 6958.623 0.173890614 90.30631 6709.731 363.700593
## 3 20 128.66379 2544.834 0.037484952 146.17279 3271.995 19.983907
## 4 4 165.72773 41620.326 1.000000000 175.16840 37827.448 -482.925932
## 5 4 88.93617 7353.541 0.080457988 99.54437 7112.907 10.905100
## 6 4 112.05057 5676.148 0.542177776 111.07084 5808.457 85.348397
## 7 36 81.65678 25858.208 0.046616700 91.00669 24534.590 18.093643
## 8 28 83.09148 3740.271 0.067520522 81.51580 3552.578 10.342763
## 9 20 50.03808 10315.067 0.112159788 46.92726 10408.876 89.999032
## 10 61 118.63991 19716.386 0.002128261 448.24067 22475.523 148.569114
## 11 12 112.69376 7825.842 0.120900205 111.35251 8246.742 8.517529
## 12 4 114.25455 4549.325 0.270522244 115.30359 4649.753 138.273264
## 13 53 76.44304 36001.512 0.001770864 449.69310 36952.772 72.398280
## 14 4 156.77118 12550.621 0.160442388 163.67998 12219.653 7.331134
## 15 12 138.18906 7172.315 0.128816656 140.40366 6708.294 6.757345
## 16 44 81.46870 54914.347 0.213015853 65.31334 54473.582 28.458298
## k L mse_log order
## 1 3.464302e+01 70.09371 9946.410 1
## 2 8.269970e-03 1208.39199 7001.082 1
## 3 4.240640e+01 129.27685 2524.216 1
## 4 -3.123327e-03 1034.87260 40160.705 1
## 5 1.797476e-01 98.06366 7095.079 1
## 6 -3.362002e-02 143.13554 5558.645 1
## 7 1.365371e+01 91.89385 23174.993 1
## 8 6.907865e-02 83.96143 3534.144 1
## 9 9.606431e-01 289.88433 11966.907 2
## 10 1.000000e+01 585.69114 24684.184 2
## 11 3.223467e+01 113.30476 7274.839 2
## 12 8.285432e-04 241.80361 3650.135 2
## 13 6.567408e+01 117.35588 35715.443 2
## 14 4.752093e+01 162.73248 11884.853 2
## 15 1.765904e+01 139.48680 5765.739 2
## 16 -3.209091e+01 121.50796 53998.968 2We then use the MSEs to calculate AIC values and generate relative log-likelihoods for each participant. This produces values that we can compare across the three functions for each participant. The likelihoods are shown below. A value of 1 indicates the function with the best fit.
read.csv('data/pilot/participant_model_likelihoods.csv')## participant loglikelihood_step loglikelihood_expl loglikelihood_log
## 1 p001_ROT_1 0.8613266 1.0000000 0.3592300
## 2 p002_ROT_1 0.5525864 1.0000000 0.3825699
## 3 p003_ROT_1 0.9373731 1.0000000 0.3780560
## 4 p004_ROT_1 0.8578013 1.0000000 0.4158283
## 5 p005_ROT_1 0.7620954 1.0000000 0.3926451
## 6 p006_ROT_1 0.7619253 1.0000000 0.3781427
## 7 p007_ROT_1 1.0000000 0.9946024 0.3974519
## 8 p008_ROT_1 0.7341245 1.0000000 0.3797855
## 9 p001_ROT_2 0.4903711 1.0000000 0.4450860
## 10 p002_ROT_2 1.0000000 0.9414584 0.3948686
## 11 p003_ROT_2 0.8678898 1.0000000 0.3844668
## 12 p004_ROT_2 1.0000000 0.9700955 0.4130507
## 13 p005_ROT_2 1.0000000 0.9542928 0.3776891
## 14 p006_ROT_2 0.9593610 1.0000000 0.3532640
## 15 p007_ROT_2 0.9944173 1.0000000 0.3644121
## 16 p008_ROT_2 0.8028875 1.0000000 0.3867287
## 17 p001_MIR_1 1.0000000 0.9683254 0.3712843
## 18 p002_MIR_1 0.9642325 1.0000000 0.3525701
## 19 p003_MIR_1 1.0000000 0.7777622 0.3708843
## 20 p004_MIR_1 0.9088696 1.0000000 0.3465064
## 21 p005_MIR_1 0.9672765 1.0000000 0.3688038
## 22 p006_MIR_1 1.0000000 0.9772213 0.3756559
## 23 p007_MIR_1 0.9488124 1.0000000 0.3894617
## 24 p008_MIR_1 0.9498184 1.0000000 0.3697983
## 25 p001_MIR_2 1.0000000 0.9909877 0.3170996
## 26 p002_MIR_2 1.0000000 0.8772382 0.2938421
## 27 p003_MIR_2 1.0000000 0.9489616 0.3957429
## 28 p004_MIR_2 1.0000000 0.9784013 0.4585044
## 29 p005_MIR_2 1.0000000 0.9742574 0.3708260
## 30 p006_MIR_2 0.9736294 1.0000000 0.3782427
## 31 p007_MIR_2 0.9353039 1.0000000 0.4280186
## 32 p008_MIR_2 0.9919736 1.0000000 0.3711129We observe that for majority of participants, the exponential function fits their data best. While we have some participants that show that the step function fits their data best, these likelihoods are not significantly far off from likelihoods in the exponential function. Furthermore, when we pool data across participants and just compare likelihoods for each perturbation type, we observe that the exponential function is the best fit for the data.
read.csv('data/pilot/all_model_likelihoods.csv')## group loglikelihood_step loglikelihood_expl loglikelihood_log
## 1 ROT 0.9175872 1 0.3887772
## 2 MIR 0.9940970 1 0.3698836Thus, we use the exponential function to compare learning rates and asymptotes between order effects conditions, and to compare rotation and mirror reversal perturbations.
Perturbation Axis
Next, we tested for any effects depending on which axis each perturbation was experienced. That is, we compared learning rates and asymptotes between half of the participants that experienced the rotation/mirror reversal on the vertical midline axis, with the other half that experienced the rotation/mirror reversal on the horizontal axis.
Rotation
plotNIROTAxisEffects()
getLambdaAxisEffectsTTest(perturbation = 'ROT')## Frequentist t-test (perturbation: ROT, condition: horizontal vs. vertical):
##
## Welch Two Sample t-test
##
## data: subdat1 and subdat2
## t = 0.075719, df = 9.3811, p-value = 0.9412
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -0.1493674 0.1597794
## sample estimates:
## mean of x mean of y
## 0.1371307 0.1319247
##
## Bayesian t-test (perturbation: ROT, condition: horizontal vs. vertical):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.4284234 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZSgetAsymptoteAxisEffectsTTest(perturbation = 'ROT')## Frequentist t-test (perturbation: ROT, condition: horizontal vs. vertical):
##
## Welch Two Sample t-test
##
## data: subdat1 and subdat2
## t = -0.32597, df = 13.332, p-value = 0.7495
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -16.20265 11.94481
## sample estimates:
## mean of x mean of y
## 80.57179 82.70071
##
## Bayesian t-test (perturbation: ROT, condition: horizontal vs. vertical):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.4433759 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZSThere are no axis effects, regardless of whether the perturbation is experienced on the horizontal or vertical axis of the workspace.
Mirror reversal
We also test for axis effects with the mirror reversed perturbation.
plotNIMIRAxisEffects()
getLambdaAxisEffectsTTest(perturbation = 'MIR')## Frequentist t-test (perturbation: MIR, condition: horizontal vs. vertical):
##
## Welch Two Sample t-test
##
## data: subdat1 and subdat2
## t = 0.70209, df = 10.758, p-value = 0.4975
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -0.1930714 0.3732157
## sample estimates:
## mean of x mean of y
## 0.2356096 0.1455375
##
## Bayesian t-test (perturbation: MIR, condition: horizontal vs. vertical):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.5050626 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZSgetAsymptoteAxisEffectsTTest(perturbation = 'MIR')## Frequentist t-test (perturbation: MIR, condition: horizontal vs. vertical):
##
## Welch Two Sample t-test
##
## data: subdat1 and subdat2
## t = -1.1488, df = 7.6784, p-value = 0.2852
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -209.11326 70.71935
## sample estimates:
## mean of x mean of y
## 115.7796 184.9765
##
## Bayesian t-test (perturbation: MIR, condition: horizontal vs. vertical):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.6616324 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZSWe also do not find axis effects for the mirror reversal perturbation.
Target location relative to axis
There were six targets for each axis. Three of the six targets were on either end of the axis, but could be on its negative (before axis) or positive (after axis) side.
Rotation
plotNIROTTargetEffects()
For the statistical tests, we calculated a sign flip for targets that required a negative amount of compensation, such that we only compared the magnitude of the compensation. These values were then used to generate the exponential function fit parameters.
getLambdaTargetEffectsTTest(perturbation = 'ROT')## Frequentist t-test (perturbation: ROT, condition: after vs. before):
##
## Welch Two Sample t-test
##
## data: subdat1 and subdat2
## t = -1.1508, df = 7.9951, p-value = 0.2831
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -0.22722622 0.07594933
## sample estimates:
## mean of x mean of y
## 0.0967085 0.1723469
##
## Bayesian t-test (perturbation: ROT, condition: after vs. before):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.6625753 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZSgetAsymptoteTargetEffectsTTest(perturbation = 'ROT')## Frequentist t-test (perturbation: ROT, condition: after vs. before):
##
## Welch Two Sample t-test
##
## data: subdat1 and subdat2
## t = 0.38122, df = 13.933, p-value = 0.7088
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -11.50821 16.48087
## sample estimates:
## mean of x mean of y
## 82.87942 80.39309
##
## Bayesian t-test (perturbation: ROT, condition: after vs. before):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.4493055 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZSWe do not find any differences between learning rates and asymptotes, suggesting that there are no target location effects.
Mirror
plotNIMIRTargetEffects()
We again calculated a sign flip for targets that required a negative amount of compensation, then used these values to generate the exponential function fit parameters.
getLambdaTargetEffectsTTest(perturbation = 'MIR')## Frequentist t-test (perturbation: MIR, condition: after vs. before):
##
## Welch Two Sample t-test
##
## data: subdat1 and subdat2
## t = 1.9561, df = 7.2705, p-value = 0.0898
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -0.04520438 0.49775895
## sample estimates:
## mean of x mean of y
## 0.30371221 0.07743493
##
## Bayesian t-test (perturbation: MIR, condition: after vs. before):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 1.410721 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZSgetAsymptoteTargetEffectsTTest(perturbation = 'MIR')## Frequentist t-test (perturbation: MIR, condition: after vs. before):
##
## Welch Two Sample t-test
##
## data: subdat1 and subdat2
## t = 0.189, df = 13.988, p-value = 0.8528
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -123.0843 146.8714
## sample estimates:
## mean of x mean of y
## 156.3249 144.4313
##
## Bayesian t-test (perturbation: MIR, condition: after vs. before):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.432839 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZSWe do not find any differences between learning rates and asymptotes in frequentist tests, suggesting that there are no target locations effects. However, the Bayesian t-test comparing learning rates between target locations suggests anecdotal evidence for a target location effect. This is likely due to the variability in compensations during initial trials of learning.
Learning Rates
As learning in the two perturbation types is independent of one another, we can then compare the progression of learning across trials between the rotation and mirror tasks. For the plots below, the y-axis will be the amount of compensation in percentage. This is because while the rotation magnitude is consistently 30-degrees, angular reach deviations for the mirror will differ depending on the target distance from the mirror axis. The mirror task will require reach deviations of 15, 30, or 45 degrees. Here, 100% would mean perfect compensation, 0% would be no compensation or reaching directly to the target, and negative values are compensations in the wrong direction relative to the target.
plotPTypeLearningCurves(group='noninstructed')
We observe that although participants learned to compensate for both perturbation types, learning in the mirror reversed perturbation had a larger variability. We look into this further and show individual performance across blocks of six trials each.
plotCollapsedBlockedIndLC(group = 'noninstructed')
To compare learning between the two perturbation types, we fit the exponential decay function to data for each perturbation type. The function produced two measures, a rate of change and asymptote of learning. We then conducted a t-test to compare both measures between the two perturbation types.
getLambdaLearningCurvesTTest()## Frequentist t-test (Rotation vs. Mirror):
##
## Welch Two Sample t-test
##
## data: subdat1 and subdat2
## t = -0.78642, df = 22.731, p-value = 0.4397
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -0.20356993 0.09147824
## sample estimates:
## mean of x mean of y
## 0.1345277 0.1905736
##
## Bayesian t-test (Rotation vs. Mirror):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.426142 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZSgetAsymptoteLearningCurvesTTest()## Frequentist t-test (Rotation vs. Mirror):
##
## Welch Two Sample t-test
##
## data: subdat1 and subdat2
## t = -2.2465, df = 15.325, p-value = 0.03981
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -133.844175 -3.639459
## sample estimates:
## mean of x mean of y
## 81.63625 150.37807
##
## Bayesian t-test (Rotation vs. Mirror):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 2.145177 ±0.01%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZSWe do not find an effect for the rate of change in learning, suggesting no difference in the progression of learning between the two perturbation types. However, we do find an effect in the asymptote of learning, suggesting that learning asymptote for the mirror reversal was higher than in the rotation.
Supplementary: Learning across three mirror target locations
Given the variability in learning for the mirror reversed perturbation, we investigated whether learning was dependent on the three different target locations.
First, we looked into the overall distribution of percentages of compensation per target location.
getTargetCurveVioplots(group='noninstructed', maxppid=15, location='maxvel')
The distributions are overall as expected, i.e. there were no bimodal distributions. We then plot angular reach deviations per target location.
plotNIMIRTargetCurve()
Although participants learned to compensate for all three target locations, it seems that variability for the target near the mirror axis (15 degrees) is larger. Therefore, we conducted the same analyses as in the previous section but removed all targets where participants had to deviate by 15 degrees.
plotPTypeLearningCurvesWONear()
Removing the 15 degree targets produced less variability, but learning in the mirror reversal still had a larger variability than the rotation.
getLambdaLearningCurvesWONearTTest()## Frequentist t-test (Rotation vs. Mirror):
##
## Welch Two Sample t-test
##
## data: subdat1 and subdat2
## t = -1.083, df = 22.465, p-value = 0.2903
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -0.2656091 0.0832296
## sample estimates:
## mean of x mean of y
## 0.1901400 0.2813298
##
## Bayesian t-test (Rotation vs. Mirror):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.5257425 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZSgetAsymptoteLearningCurvesWONearTTest()## Frequentist t-test (Rotation vs. Mirror):
##
## Welch Two Sample t-test
##
## data: subdat1 and subdat2
## t = -1.669, df = 15.243, p-value = 0.1155
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -164.90019 19.95178
## sample estimates:
## mean of x mean of y
## 86.08078 158.55499
##
## Bayesian t-test (Rotation vs. Mirror):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.9563318 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZSWe conducted the same t-tests to compare learning rates and asymptotes between the two perturbation types. We found that after removing the 15 degree target, there are no effects in rate and asymptote, suggesting that the 15 degree target contributed to higher asymptotes in learning the mirror reversed perturbation.
Reach aftereffects
We then use washout trials following perturbation training to investigate whether reach aftereffects are observed. We expected to observe reach aftereffects following rotation training, but not mirror reversal training.
plotPTypeAftereffects()
We can also show individual performance across blocks of six trials each.
plotCollapsedBlockedIndRAE()
We observe aftereffects following rotation training but not after mirror reversal training. This is supported by looking into the individual targets for the mirror reversal. Angular reach deviations show that the rate of de-adaptation is around zero across washout trials.
plotNIRAETargetCurve()
It is possible to fit an exponential decay function to the washout data, where it starts at the asymptote and approaches zero over time. The exponential function can be fit into washout trials following rotation training. However, given that the washout trials after mirror reversal training are around zero, it would not make sense to fit the function to this data.
plotROTRAEModel(groups='noninstructed')
plotMIRRAEModel(groups='noninstructed')
We therefore confirmed the presence of reach aftereffects by comparing the percentages of compensation during the last block of aligned reaches with the first block of each of the corresponding washout trials after rotated and mirror reversed training.
RAEt.test(group='noninstructed')## Aligned (last block) compared to Rotation Washout (first block):
##
## Paired t-test
##
## data: ALdat$compensation and ROTdat$compensation
## t = -8.5651, df = 15, p-value = 3.679e-07
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
## -57.85656 -34.79894
## sample estimates:
## mean difference
## -46.32775
##
## Effect Size - Cohen d:
## [1] 3.180562
## Bayesian t-test Aligned (last block) compared to Rotation Washout (first block):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 12748734 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Aligned (last block) compared to Mirror Washout (first block):
##
## Paired t-test
##
## data: ALdat$compensation and MIRdat$compensation
## t = -2.0185, df = 15, p-value = 0.06178
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
## -28.1993350 0.7673049
## sample estimates:
## mean difference
## -13.71602
##
## Effect Size - Cohen d:
## [1] 0.6798059
## Bayesian t-test Aligned (last block) compared to Mirror Washout (first block):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 1.330114 ±0.01%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Rotation Washout (first block) compared to Mirror Washout (first block):
##
## Paired t-test
##
## data: ROTdat$compensation and MIRdat$compensation
## t = 3.9384, df = 15, p-value = 0.001314
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
## 14.96254 50.26093
## sample estimates:
## mean difference
## 32.61174
##
## Effect Size - Cohen d:
## [1] 1.361953
## Bayesian t-test Rotation Washout (first block) compared to Mirror Washout (first block):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 48.93883 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZSWe find an effect between aligned and rotated blocks, but not between aligned and mirror reversed blocks, confirming our expectations that aftereffects are only observed following rotation training. Moreover, we find an effect between the first washout blocks following rotation and mirror reversed training. We then compared the corresponding washout trials of rotation and mirror reversed training during the first, second, and last blocks of trials (trials 1-6, 7-12, 43-48).
reachaftereffectsANOVA(group='noninstructed')## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 perturbtype 1 15 10.03195 6.376323e-03 * 0.1782152
## 3 block 2 30 18.24462 6.539565e-06 * 0.1396883
## 4 perturbtype:block 2 30 16.11864 1.762222e-05 * 0.1481931
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.6020397 0.028666577 *
## 4 perturbtype:block 0.4964129 0.007428502 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 block 0.7153279 9.00959e-05 * 0.7697679 5.444034e-05
## 4 perturbtype:block 0.6650762 2.82235e-04 * 0.7052909 2.018786e-04
## p[HF]<.05
## 3 *
## 4 *reachaftereffectsBayesANOVA(group='noninstructed')## Bayes factor analysis
## --------------
## [1] perturbtype + participant : 502.993 ±1.3%
## [2] block + participant : 16.07881 ±0.68%
## [3] perturbtype + block + participant : 24704.81 ±1.08%
## [4] perturbtype + block + perturbtype:block + participant : 7823228 ±2.36%
##
## Against denominator:
## compensation ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## perturbtype 0.60 1.00 3.06e+05
## block 0.60 1.00 1.04e+04
## block:perturbtype 0.20 1.00 1.24e+03
##
## * Compared among: all models
## * Priors odds: uniform-equalWe find a significant perturbation type by block interaction.
RAEComparisonsAllBlocksEffSize(group='noninstructed')## contrast estimate SE df t.ratio p.value
## Block1: MIR vs. Block2: MIR 5.326 5.06 15 1.053 1.0000
## Block1: MIR vs. Block3: MIR -0.203 6.87 15 -0.030 1.0000
## Block1: ROT vs. Block2: ROT 15.838 3.10 15 5.110 0.0009
## Block1: ROT vs. Block3: ROT 36.074 4.06 15 8.877 <.0001
## Block1: ROT vs. MIR -32.612 8.28 15 -3.938 0.0092
## Block2: ROT vs. MIR -22.099 5.30 15 -4.170 0.0058
## Block3: ROT vs. MIR 3.665 5.76 15 0.637 1.0000
##
## P value adjustment: bonferroni method for 7 tests
## contrast etasquared
## 1 Block1: MIR vs. Block2: MIR 6.884968e-02
## 2 Block1: MIR vs. Block3: MIR 5.823273e-05
## 3 Block1: ROT vs. Block2: ROT 6.351304e-01
## 4 Block1: ROT vs. Block3: ROT 8.400960e-01
## 5 Block1: ROT vs. MIR 5.083788e-01
## 6 Block2: ROT vs. MIR 5.368444e-01
## 7 Block3: ROT vs. MIR 2.630462e-02reachaftereffectsBayesfollowup(group='noninstructed')## Bayesian t-test Mirror block 1 vs block 2:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.3972204 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test Mirror block 1 vs last block:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.3362827 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test Rotation block 1 vs block 2:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 3.335568 ±0.01%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test Rotation block 1 vs last block:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 22218.73 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test Rotation block 1 vs Mirror block 1:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 48.93883 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test Rotation block 2 vs Mirror block 2:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 46.47629 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test Rotation last block vs Mirror last block:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.4028267 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZSFollow up tests confirm that the first and second rotation washout blocks are different from the first and second mirror washout blocks.
Supplementary: Training rate of learning and its association with aftereffects
We also wanted to test whether learning rates during training correlate to the aftereffects, or lack thereof, during washout trials. To do this, we conducted correlation tests that compared the rate of change during learning with the compensation percentages during the first block of washout trials.
getLambdaRAECorrelations(group='noninstructed')##
## Pearson's product-moment correlation
##
## data: MIRfirst$lambda and MIRfirst$compensation
## t = -0.04915, df = 14, p-value = 0.9615
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.5055484 0.4857333
## sample estimates:
## cor
## -0.01313462
##
##
## Pearson's product-moment correlation
##
## data: ROTfirst$lambda and ROTfirst$compensation
## t = -0.40671, df = 14, p-value = 0.6904
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.5730698 0.4095834
## sample estimates:
## cor
## -0.108062
##
## Bayes factor analysis
## --------------
## [1] Alt., r=0.333 : 0.5194012 ±0%
##
## Against denominator:
## Null, rho = 0
## ---
## Bayes factor type: BFcorrelation, Jeffreys-beta*
##
## Bayes factor analysis
## --------------
## [1] Alt., r=0.333 : 0.5510508 ±0%
##
## Against denominator:
## Null, rho = 0
## ---
## Bayes factor type: BFcorrelation, Jeffreys-beta*We do not find significant relationships between learning rates and corresponding aftereffects.
Movement analyses
We compared other behavioral measures associated with reaching movements in both perturbation types.
Reaction time
We defined reaction time (RT) as the time elapsed between the go signal onset and when the hand-cursor has moved 0.5 cm away from the start position.
plotNIBlockedRT()
To quantify changes in RT across rotation and mirror reversed training, we conducted t-tests to compare RTs in the last block of aligned reaches with the RTs in the first and last blocks of rotation or mirror reversed reaches. We also conducted t-tests to compare RTs in the last block of aligned reaches with the RTs in the first blocks of washout reaches following each perturbation training.
RTt.test(group='noninstructed')## Aligned (last block) compared to Rotation (first block):
##
## Paired t-test
##
## data: ALdat$compensation and ROTdat$compensation
## t = -3.1381, df = 15, p-value = 0.00677
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
## -60.26283 -11.51174
## sample estimates:
## mean difference
## -35.88729
##
## Effect Size - Cohen d:
## [1] 0.6072004
## Bayesian t-test Aligned (last block) compared to Rotation (first block):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 1.01522 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Aligned (last block) compared to Mirror (first block):
##
## Paired t-test
##
## data: ALdat$compensation and MIRdat$compensation
## t = -7.6317, df = 15, p-value = 1.531e-06
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
## -392.4082 -221.0708
## sample estimates:
## mean difference
## -306.7395
##
## Effect Size - Cohen d:
## [1] 2.613546
## Bayesian t-test Aligned (last block) compared to Mirror (first block):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 282927.2 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Aligned (last block) compared to Rotation Washout (first block):
##
## Paired t-test
##
## data: ALdat$compensation and ROTWASHdat$compensation
## t = 1.2824, df = 15, p-value = 0.2192
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
## -10.53517 42.35997
## sample estimates:
## mean difference
## 15.9124
##
## Effect Size - Cohen d:
## [1] 0.3791996
## Bayesian t-test Aligned (last block) compared to Rotation Washout (first block):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.5213094 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Aligned (last block) compared to Mirror Washout (first block):
##
## Paired t-test
##
## data: ALdat$compensation and MIRWASHdat$compensation
## t = -0.88032, df = 15, p-value = 0.3926
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
## -41.23091 17.12780
## sample estimates:
## mean difference
## -12.05156
##
## Effect Size - Cohen d:
## [1] 0.2145698
## Bayesian t-test Aligned (last block) compared to Mirror Washout (first block):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.3873179 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Aligned (last block) compared to Rotation (last block):
##
## Paired t-test
##
## data: ALdat$compensation and ROTdatlast$compensation
## t = 0.073926, df = 15, p-value = 0.942
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
## -33.94379 36.38297
## sample estimates:
## mean difference
## 1.21959
##
## Effect Size - Cohen d:
## [1] 0.02475069
## Bayesian t-test Aligned (last block) compared to Rotation (last block):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.33684 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Aligned (last block) compared to Mirror (last block):
##
## Paired t-test
##
## data: ALdat$compensation and MIRdatlast$compensation
## t = -2.5865, df = 15, p-value = 0.02065
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
## -77.877302 -7.511019
## sample estimates:
## mean difference
## -42.69416
##
## Effect Size - Cohen d:
## [1] 0.6554177
## Bayesian t-test Aligned (last block) compared to Mirror (last block):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 1.211139 ±0.01%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZSAs expected, participants were slower in initiating movements in the first block of perturbation training, regardless of the perturbation type. However, we do see in the plot that participants were slower to initiate movements in mirror reversed reaches compared to rotated reaches. RTs taper off and go back to baseline levels for rotated reaches, but is still significantly slower than baseline levels for mirror reversed reaches at the end of training. There are no effects between aligned and washout reaches.
We also compared RTs between rotation and mirror reversed reaches across training trials.
reactiontimeANOVA(group='noninstructed')## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 perturbtype 1 15 46.37509 5.892717e-06 * 0.3841103
## 3 block 2 30 22.38240 1.125541e-06 * 0.2526722
## 4 perturbtype:block 2 30 11.51226 1.948353e-04 * 0.1608922
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.8561149 0.3370733
## 4 perturbtype:block 0.9233985 0.5724323
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 block 0.8742137 4.417721e-06 * 0.9800662 1.397428e-06
## 4 perturbtype:block 0.9288488 2.984089e-04 * 1.0547300 1.948353e-04
## p[HF]<.05
## 3 *
## 4 *RTBayesANOVA(group='noninstructed')## Bayes factor analysis
## --------------
## [1] perturbtype + participant : 3634957 ±1.08%
## [2] block + participant : 160.5118 ±1.3%
## [3] perturbtype + block + participant : 38091142801 ±1.17%
## [4] perturbtype + block + perturbtype:block + participant : 1.347205e+13 ±3.37%
##
## Against denominator:
## compensation ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## perturbtype 0.60 1.00 5.58e+10
## block 0.60 1.00 2.48e+06
## block:perturbtype 0.20 1.00 1.41e+03
##
## * Compared among: all models
## * Priors odds: uniform-equalWe find a significant perturbation type by block interaction.
RTComparisonsAllBlocksEffSize(group='noninstructed')## contrast estimate SE df t.ratio p.value
## Block1: ROT vs. MIR 270.9 38.7 15 7.000 <.0001
## Block2: ROT vs. MIR 196.2 48.4 15 4.053 0.0031
## Block3: ROT vs. MIR 43.9 19.0 15 2.311 0.1064
##
## P value adjustment: bonferroni method for 3 tests
## contrast etasquared
## 1 Block1: ROT vs. MIR 0.7656395
## 2 Block2: ROT vs. MIR 0.5227581
## 3 Block3: ROT vs. MIR 0.2625601RTBayesfollowup(group='noninstructed')## Bayesian t-test Rotation block 1 vs Mirror block 1:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 14625.19 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test Rotation block 2 vs Mirror block 2:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 115.1938 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test Rotation last block vs Mirror last block:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 1.150233 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZSFollow up tests show that rotation and mirror reversed RTs differed during the first and second blocks of training, and Bayesian tests showed anecdotal evidence of an effect between perturbation RTs in the last block of training. Overall, this shows that movement initiation is slower during mirror reversed perturbed reaches, compared to rotation perturbation reaches.
Movement time
We defined movement time (MT) as the time elapsed between the first sample when the hand-cursor is >0.5 cm away from the start position and the first sample when the hand-cursor is greater than the start-to-target distance
plotNIBlockedMT()
To quantify changes in MT across rotation and mirror reversed training, we conducted the same t-tests as in the reaction time analysis. We compared MTs in the last block of aligned reaches with the MTs in the first and last blocks of rotation or mirror reversed reaches. We also conducted t-tests to compare MTs in the last block of aligned reaches with the MTs in the first blocks of washout reaches following each perturbation training.
MTt.test(group='noninstructed')## Aligned (last block) compared to Rotation (first block):
##
## Paired t-test
##
## data: ALdat$compensation and ROTdat$compensation
## t = 3.5038, df = 15, p-value = 0.003198
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
## 13.36498 54.87910
## sample estimates:
## mean difference
## 34.12204
##
## Effect Size - Cohen d:
## [1] 0.8538119
## Bayesian t-test Aligned (last block) compared to Rotation (first block):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 2.817218 ±0.01%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Aligned (last block) compared to Mirror (first block):
##
## Paired t-test
##
## data: ALdat$compensation and MIRdat$compensation
## t = -0.18063, df = 15, p-value = 0.8591
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
## -56.97808 48.07529
## sample estimates:
## mean difference
## -4.451395
##
## Effect Size - Cohen d:
## [1] 0.04928006
## Bayesian t-test Aligned (last block) compared to Mirror (first block):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.338732 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Aligned (last block) compared to Rotation Washout (first block):
##
## Paired t-test
##
## data: ALdat$compensation and ROTWASHdat$compensation
## t = 2.6516, df = 15, p-value = 0.01813
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
## 5.243939 48.221812
## sample estimates:
## mean difference
## 26.73288
##
## Effect Size - Cohen d:
## [1] 0.6088755
## Bayesian t-test Aligned (last block) compared to Rotation Washout (first block):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 1.02126 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Aligned (last block) compared to Mirror Washout (first block):
##
## Paired t-test
##
## data: ALdat$compensation and MIRWASHdat$compensation
## t = 1.9364, df = 15, p-value = 0.07189
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
## -1.80499 37.64532
## sample estimates:
## mean difference
## 17.92017
##
## Effect Size - Cohen d:
## [1] 0.416283
## Bayesian t-test Aligned (last block) compared to Mirror Washout (first block):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.5696985 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Aligned (last block) compared to Rotation (last block):
##
## Paired t-test
##
## data: ALdat$compensation and ROTdatlast$compensation
## t = 2.6135, df = 15, p-value = 0.01957
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
## 4.473732 44.038268
## sample estimates:
## mean difference
## 24.256
##
## Effect Size - Cohen d:
## [1] 0.5427241
## Bayesian t-test Aligned (last block) compared to Rotation (last block):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.8170532 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Aligned (last block) compared to Mirror (last block):
##
## Paired t-test
##
## data: ALdat$compensation and MIRdatlast$compensation
## t = 2.4529, df = 15, p-value = 0.02689
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
## 3.46726 49.45266
## sample estimates:
## mean difference
## 26.45996
##
## Effect Size - Cohen d:
## [1] 0.5614742
## Bayesian t-test Aligned (last block) compared to Mirror (last block):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.8683503 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZSParticipants were faster in executing movements during rotated reaches, compared to aligned baseline reaches. Interestingly, faster MTs were also observed in the first block of washout trials following rotation training. In contrast, MTs do not differ between aligned reaches and the first block of mirror reversed reaches or its corresponding washout trials. However, we do find faster MTs during the last block of mirror reversed reaches, when compared to aligned reaches.
We also compared MTs between rotation and mirror reversed reaches across training trials.
movementtimePerturbANOVA(group='noninstructed')## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 perturbtype 1 14 0.86020670 0.3693952 7.423837e-03
## 3 block 2 28 0.01775302 0.9824147 8.965923e-05
## 4 perturbtype:block 2 28 1.50180740 0.2401263 9.475055e-03
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.6538806 0.0632033
## 4 perturbtype:block 0.9900824 0.9372679
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF] p[HF]<.05
## 3 block 0.7428761 0.9569098 0.8105275 0.9660618
## 4 perturbtype:block 0.9901798 0.2403111 1.1525051 0.2401263MTBayesANOVA(group='noninstructed')## Bayes factor analysis
## --------------
## [1] perturbtype + participant : 0.5067736 ±1.64%
## [2] block + participant : 0.09875632 ±0.62%
## [3] perturbtype + block + participant : 0.05046115 ±1.82%
## [4] perturbtype + block + perturbtype:block + participant : 0.01900667 ±1.64%
##
## Against denominator:
## compensation ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## perturbtype 0.60 0.34 0.350
## block 0.60 0.10 0.074
## block:perturbtype 0.20 0.01 0.046
##
## * Compared among: all models
## * Priors odds: uniform-equalWe do not find any main or interaction effects for perturbation type and block. Therefore, even though movement initiation was slower for both perturbed reaches, movement execution was faster for the rotated reaches. Mirror reversed movement times eventually became faster than aligned reaches by the end of perturbation training. This supports the idea that more explicit processes contribute to learning the mirror reversal, as both movement initiation and execution are slower for these reaches compared to rotation pertubation reaches.
Path length
We defined path length (PL) as the total distance, given x and y coordinates of the reach trajectory, traveled between movement onset and offset. Movement onset and offset are the start and end movement times defined in the previous section. The shortest path length to the target is a straight line spanning the start-to-target distance. However, movements are not perfectly straight and may travel in different directions, depending on the perturbation.
plotPTypePathLength(group='noninstructed')
Similar to the other measures above, we conducted t-tests to compare PLs between the last block of aligned trials with the first and last blocks of rotation and mirror reversed training. We then compared PLs between the two perturbation types.
PLt.test(group='noninstructed')## Aligned (last block) compared to Rotation (first block):
##
## Paired t-test
##
## data: ALdat$compensation and ROTdat$compensation
## t = 1.8039, df = 15, p-value = 0.09136
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
## -0.02151242 0.25849772
## sample estimates:
## mean difference
## 0.1184927
##
## Effect Size - Cohen d:
## [1] 0.5589686
## Bayesian t-test Aligned (last block) compared to Rotation (first block):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.8612201 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Aligned (last block) compared to Mirror (first block):
##
## Paired t-test
##
## data: ALdat$compensation and MIRdat$compensation
## t = 0.45273, df = 15, p-value = 0.6572
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
## -0.4456104 0.6859617
## sample estimates:
## mean difference
## 0.1201756
##
## Effect Size - Cohen d:
## [1] 0.1635101
## Bayesian t-test Aligned (last block) compared to Mirror (first block):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.3650481 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Aligned (last block) compared to Rotation (last block):
##
## Paired t-test
##
## data: ALdat$compensation and ROTdatlast$compensation
## t = 1.0801, df = 15, p-value = 0.2971
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
## -0.08026114 0.24517995
## sample estimates:
## mean difference
## 0.0824594
##
## Effect Size - Cohen d:
## [1] 0.4003611
## Bayesian t-test Aligned (last block) compared to Rotation (last block):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.5478674 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Aligned (last block) compared to Mirror (last block):
##
## Paired t-test
##
## data: ALdat$compensation and MIRdatlast$compensation
## t = 1.5556, df = 15, p-value = 0.1407
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
## -0.05870654 0.37585698
## sample estimates:
## mean difference
## 0.1585752
##
## Effect Size - Cohen d:
## [1] 0.5078908
## Bayesian t-test Aligned (last block) compared to Mirror (last block):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.7333267 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZSpathlengthPerturbANOVA(group='noninstructed')## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 perturbtype 1 15 0.1108586 0.7437769 0.001741464
## 3 block 2 30 0.7518656 0.4801633 0.009738404
## 4 perturbtype:block 2 30 0.7422843 0.4845656 0.013294868
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.5018114 0.008012787 *
## 4 perturbtype:block 0.6308852 0.039778851 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF] p[HF]<.05
## 3 block 0.6674727 0.4333219 0.7083443 0.4402371
## 4 perturbtype:block 0.7303989 0.4474950 0.7892919 0.4566603PLBayesANOVA(group='noninstructed')## Bayes factor analysis
## --------------
## [1] perturbtype + participant : 0.2434858 ±5.38%
## [2] block + participant : 0.1459601 ±0.62%
## [3] perturbtype + block + participant : 0.03507589 ±1.99%
## [4] perturbtype + block + perturbtype:block + participant : 0.009267227 ±3.48%
##
## Against denominator:
## compensation ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## perturbtype 0.60 0.20 0.167
## block 0.60 0.13 0.102
## block:perturbtype 0.20 6.46e-03 0.026
##
## * Compared among: all models
## * Priors odds: uniform-equalWe do not find any effects across all comparisons, suggesting that the path of reach trajectories did not differ regardless of trial type or perturbation type.
Instructed participants
For the instructed participants, we told them about the nature of each perturbation. We let them know that the rotation will be 30-degree rotation (CW or CCW depending on their ID), and that the mirror reversal will be dependent on which axis the mirror is placed. We also showed them animations of how to compensate for each perturbation type, and tested their understanding of the strategy by having them draw on a clock-face the location that they should move to bring a cursor to the target. For example, if the target is at 2 o’clock, then they had to draw an arrow to 1 o’clock to correct for a 30 degree CW rotation. In contrast, for a mirror placed along the vertical midline, a target at 2 o’clock would mean that they had to draw an arrow to the 10 position. We know from previous work that such instructions provide an advantage in early learning for rotation perturbations, and we wanted to test whether the same advantage will be observed for the mirror reversal.
plotPTypeLearningCurves(group='instructed')
plotCollapsedBlockedIndLC(group='instructed', maxppid=31)
We find that instructions did provide an advantage during the first few trials of training for both perturbation types, and that participants were immediately performing around perfect compensation. There was no change in learning across training, but we do find that mirror reversed reaches showed more variability.
Reach aftereffects
We then investigated the corresponding washout trials for the instructed participants.
plotPTypeAftereffects(group='instructed')
plotCollapsedBlockedIndRAE(group='instructed', maxppid=31)
We repeated the reach aftereffects analyses we conducted for non-instructed participants with the instructed participants.
RAEt.test(group='instructed')## Aligned (last block) compared to Rotation Washout (first block):
##
## Paired t-test
##
## data: ALdat$compensation and ROTdat$compensation
## t = -6.9487, df = 15, p-value = 4.664e-06
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
## -60.37988 -32.03296
## sample estimates:
## mean difference
## -46.20642
##
## Effect Size - Cohen d:
## [1] 2.494295
## Bayesian t-test Aligned (last block) compared to Rotation Washout (first block):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 123534.6 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Aligned (last block) compared to Mirror Washout (first block):
##
## Paired t-test
##
## data: ALdat$compensation and MIRdat$compensation
## t = -2.2901, df = 15, p-value = 0.03692
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
## -29.074359 -1.043404
## sample estimates:
## mean difference
## -15.05888
##
## Effect Size - Cohen d:
## [1] 0.973542
## Bayesian t-test Aligned (last block) compared to Mirror Washout (first block):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 5.097014 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Rotation Washout (first block) compared to Mirror Washout (first block):
##
## Paired t-test
##
## data: ROTdat$compensation and MIRdat$compensation
## t = 3.7819, df = 15, p-value = 0.001809
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
## 13.59300 48.70207
## sample estimates:
## mean difference
## 31.14754
##
## Effect Size - Cohen d:
## [1] 1.394041
## Bayesian t-test Rotation Washout (first block) compared to Mirror Washout (first block):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 60.07102 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZSThe first block of washout trials following rotation training differed from the last block of aligned baseline reaches, suggesting the presence of aftereffects. Interestingly, we also find an effect when comparing the first block of washout trials following mirror reversed reaches with aligned reaches. However, aftereffects were larger for washout trials following rotation training, than those following mirror reversed training. The presence of very small aftereffects in the mirror reversal washout trials is unexpected, but could be due to being able to know how to compensate for the perturbation from the beginning of training. That is, they were exposed to training with the mirror reversal longer than the non-instructed participants.
We compare rotation and mirror reversed washout trials further.
reachaftereffectsANOVA(group='instructed')## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 perturbtype 1 15 17.552155 7.894270e-04 * 0.25469337
## 3 block 2 30 15.471313 2.415469e-05 * 0.12293176
## 4 perturbtype:block 2 30 3.523014 4.223711e-02 * 0.05530366
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.9355022 0.62706686
## 4 perturbtype:block 0.6096292 0.03129395 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 block 0.9394102 3.908057e-05 * 1.069306 2.415469e-05
## 4 perturbtype:block 0.7192326 6.065359e-02 0.774818 5.646370e-02
## p[HF]<.05
## 3 *
## 4reachaftereffectsBayesANOVA(group='instructed')## Bayes factor analysis
## --------------
## [1] perturbtype + participant : 74605.03 ±1.03%
## [2] block + participant : 6.615574 ±0.83%
## [3] perturbtype + block + participant : 2570620 ±1.99%
## [4] perturbtype + block + perturbtype:block + participant : 4280281 ±1.95%
##
## Against denominator:
## compensation ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## perturbtype 0.60 1.00 6.06e+05
## block 0.60 0.99 61.22
## block:perturbtype 0.20 0.62 6.47
##
## * Compared among: all models
## * Priors odds: uniform-equalWe find a significant perturbation type by block interaction.
RAEComparisonsAllBlocksEffSize(group='instructed')## contrast estimate SE df t.ratio p.value
## Block1: MIR vs. Block2: MIR 5.45 4.73 15 1.153 1.0000
## Block1: MIR vs. Block3: MIR 6.88 5.05 15 1.364 1.0000
## Block1: ROT vs. Block2: ROT 9.50 2.87 15 3.306 0.0336
## Block1: ROT vs. Block3: ROT 28.45 7.27 15 3.911 0.0097
## Block1: ROT vs. MIR -31.15 8.24 15 -3.782 0.0127
## Block2: ROT vs. MIR -27.09 7.59 15 -3.568 0.0196
## Block3: ROT vs. MIR -9.58 6.04 15 -1.588 0.9323
##
## P value adjustment: bonferroni method for 7 tests
## contrast etasquared
## 1 Block1: MIR vs. Block2: MIR 0.08137381
## 2 Block1: MIR vs. Block3: MIR 0.11036641
## 3 Block1: ROT vs. Block2: ROT 0.42149321
## 4 Block1: ROT vs. Block3: ROT 0.50491506
## 5 Block1: ROT vs. MIR 0.48810223
## 6 Block2: ROT vs. MIR 0.45907447
## 7 Block3: ROT vs. MIR 0.14388642reachaftereffectsBayesfollowup(group='instructed')## Bayesian t-test Mirror block 1 vs block 2:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.4289297 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test Mirror block 1 vs last block:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.5561826 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test Rotation block 1 vs block 2:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.5317184 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test Rotation block 1 vs last block:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 49.6715 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test Rotation block 1 vs Mirror block 1:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 60.07102 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test Rotation block 2 vs Mirror block 2:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 23.33725 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test Rotation last block vs Mirror last block:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 1.156555 ±0.01%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZSFollow up tests show that washout trials following rotation training show aftereffects that go back down near zero. Washout trials following mirror reversed trials, however, did not differ across blocks of trials. Thus, the small aftereffects for mirror reversed trials in the previous set of tests did not hold up here. Finally compensation in rotation washout trials were larger in the first and second blocks, compared to mirror reversed washout trials. Overall, it is clear that aftereffects are observed following rotation training only.
Movement analyses
We also compared other behavioral measures associated with reaching movements in both perturbation types for the instructed participants.
Reaction time
We defined reaction time (RT) as the time elapsed between the go signal onset and when the hand-cursor has moved 0.5 cm away from the start position.
plotIBlockedRT()
To quantify changes in RT across rotation and mirror reversed training, we conducted t-tests to compare RTs in the last block of aligned reaches with the RTs in the first and last blocks of rotation or mirror reversed reaches. We also conducted t-tests to compare RTs in the last block of aligned reaches with the RTs in the first blocks of washout reaches following each perturbation training.
RTt.test(group='instructed')## Aligned (last block) compared to Rotation (first block):
##
## Paired t-test
##
## data: ALdat$compensation and ROTdat$compensation
## t = -3.3466, df = 15, p-value = 0.004416
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
## -192.04541 -42.59921
## sample estimates:
## mean difference
## -117.3223
##
## Effect Size - Cohen d:
## [1] 1.00782
## Bayesian t-test Aligned (last block) compared to Rotation (first block):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 6.102814 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Aligned (last block) compared to Mirror (first block):
##
## Paired t-test
##
## data: ALdat$compensation and MIRdat$compensation
## t = -5.8431, df = 15, p-value = 3.235e-05
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
## -358.8209 -167.0079
## sample estimates:
## mean difference
## -262.9144
##
## Effect Size - Cohen d:
## [1] 1.830453
## Bayesian t-test Aligned (last block) compared to Mirror (first block):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 1147.438 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Aligned (last block) compared to Rotation Washout (first block):
##
## Paired t-test
##
## data: ALdat$compensation and ROTWASHdat$compensation
## t = 0.016671, df = 15, p-value = 0.9869
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
## -22.26369 22.61470
## sample estimates:
## mean difference
## 0.1755051
##
## Effect Size - Cohen d:
## [1] 0.002763145
## Bayesian t-test Aligned (last block) compared to Rotation Washout (first block):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.3362119 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Aligned (last block) compared to Mirror Washout (first block):
##
## Paired t-test
##
## data: ALdat$compensation and MIRWASHdat$compensation
## t = 1.897, df = 15, p-value = 0.07725
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
## -3.188351 54.784986
## sample estimates:
## mean difference
## 25.79832
##
## Effect Size - Cohen d:
## [1] 0.484796
## Bayesian t-test Aligned (last block) compared to Mirror Washout (first block):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.6850895 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Aligned (last block) compared to Rotation (last block):
##
## Paired t-test
##
## data: ALdat$compensation and ROTdatlast$compensation
## t = -1.2063, df = 15, p-value = 0.2464
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
## -62.53725 17.33285
## sample estimates:
## mean difference
## -22.6022
##
## Effect Size - Cohen d:
## [1] 0.2700877
## Bayesian t-test Aligned (last block) compared to Rotation (last block):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.4205158 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Aligned (last block) compared to Mirror (last block):
##
## Paired t-test
##
## data: ALdat$compensation and MIRdatlast$compensation
## t = -3.8588, df = 15, p-value = 0.001546
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
## -126.53830 -36.48861
## sample estimates:
## mean difference
## -81.51345
##
## Effect Size - Cohen d:
## [1] 0.8535032
## Bayesian t-test Aligned (last block) compared to Mirror (last block):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 2.81313 ±0.01%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZSThe results are similar to those with the noninstructed participants. Participants were slower in initiating movements in the first block of perturbation training, regardless of the perturbation type. However, we do see in the plot that participants were slower to initiate movements in mirror reversed reaches compared to rotated reaches. RTs taper off and go back to baseline levels for rotated reaches, but is still significantly slower than baseline levels for mirror reversed reaches at the end of training. There are no effects between aligned and washout reaches.
We also compared RTs between rotation and mirror reversed reaches across training trials.
reactiontimeANOVA(group='instructed')## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 perturbtype 1 15 22.242789 0.000275758 * 0.1336356
## 3 block 2 30 7.985512 0.001657892 * 0.1071339
## 4 perturbtype:block 2 30 1.619007 0.214927836 0.0245030
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.6264875 0.03787797 *
## 4 perturbtype:block 0.8348009 0.28254017
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 block 0.7280603 0.005002071 * 0.7862567 0.003944299
## 4 perturbtype:block 0.8582224 0.218883460 0.9584451 0.216156091
## p[HF]<.05
## 3 *
## 4RTBayesANOVA(group='instructed')## Bayes factor analysis
## --------------
## [1] perturbtype + participant : 305.808 ±0.89%
## [2] block + participant : 14.71921 ±1.41%
## [3] perturbtype + block + participant : 13706.39 ±1.92%
## [4] perturbtype + block + perturbtype:block + participant : 7013.034 ±1.62%
##
## Against denominator:
## compensation ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## perturbtype 0.60 1.00 891.70
## block 0.60 0.99 45.05
## block:perturbtype 0.20 0.33 2.00
##
## * Compared among: all models
## * Priors odds: uniform-equalWe find main effects for perturbation type and block.
RTComparisonsAllBlocksEffSize(group='instructed')## contrast estimate SE df t.ratio p.value
## Block1: ROT vs. MIR 145.6 47.8 15 3.045 0.0246
## Block2: ROT vs. MIR 183.7 68.1 15 2.697 0.0496
## Block3: ROT vs. MIR 58.9 19.6 15 2.999 0.0270
##
## P value adjustment: bonferroni method for 3 tests
## contrast etasquared
## 1 Block1: ROT vs. MIR 0.3819464
## 2 Block2: ROT vs. MIR 0.3266135
## 3 Block3: ROT vs. MIR 0.3748060RTBayesfollowup(group='instructed')## Bayesian t-test Rotation block 1 vs Mirror block 1:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 2.546268 ±0.01%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test Rotation block 2 vs Mirror block 2:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 3.176157 ±0.01%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test Rotation last block vs Mirror last block:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.7744694 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZSFollow up tests show that rotation and mirror reversed RTs differed across block of training. Overall, this confirms that movement initiation is slower during mirror reversed perturbed reaches, compared to rotation perturbation reaches.
Movement time
We defined movement time (MT) as the time elapsed between the first sample when the hand-cursor is >0.5 cm away from the start position and the first sample when the hand-cursor is greater than the start-to-target distance
plotIBlockedMT()
To quantify changes in MT across rotation and mirror reversed training, we conducted the same t-tests as in the reaction time analysis. We compared MTs in the last block of aligned reaches with the MTs in the first and last blocks of rotation or mirror reversed reaches. We also conducted t-tests to compare MTs in the last block of aligned reaches with the MTs in the first blocks of washout reaches following each perturbation training.
MTt.test(group='instructed')## Aligned (last block) compared to Rotation (first block):
##
## Paired t-test
##
## data: ALdat$compensation and ROTdat$compensation
## t = -0.026051, df = 15, p-value = 0.9796
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
## -23.84831 23.27238
## sample estimates:
## mean difference
## -0.287964
##
## Effect Size - Cohen d:
## [1] 0.005575588
## Bayesian t-test Aligned (last block) compared to Rotation (first block):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.3362362 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Aligned (last block) compared to Mirror (first block):
##
## Paired t-test
##
## data: ALdat$compensation and MIRdat$compensation
## t = -1.7657, df = 15, p-value = 0.09779
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
## -75.671969 7.102291
## sample estimates:
## mean difference
## -34.28484
##
## Effect Size - Cohen d:
## [1] 0.4986822
## Bayesian t-test Aligned (last block) compared to Mirror (first block):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.7134489 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Aligned (last block) compared to Rotation Washout (first block):
##
## Paired t-test
##
## data: ALdat$compensation and ROTWASHdat$compensation
## t = 0.7855, df = 15, p-value = 0.4444
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
## -14.02251 30.38971
## sample estimates:
## mean difference
## 8.183598
##
## Effect Size - Cohen d:
## [1] 0.1558709
## Bayesian t-test Aligned (last block) compared to Rotation Washout (first block):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.3623215 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Aligned (last block) compared to Mirror Washout (first block):
##
## Paired t-test
##
## data: ALdat$compensation and MIRWASHdat$compensation
## t = 1.1782, df = 15, p-value = 0.2571
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
## -9.692121 33.651818
## sample estimates:
## mean difference
## 11.97985
##
## Effect Size - Cohen d:
## [1] 0.2537737
## Bayesian t-test Aligned (last block) compared to Mirror Washout (first block):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.4096897 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Aligned (last block) compared to Rotation (last block):
##
## Paired t-test
##
## data: ALdat$compensation and ROTdatlast$compensation
## t = 1.0866, df = 15, p-value = 0.2944
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
## -12.99002 40.00618
## sample estimates:
## mean difference
## 13.50808
##
## Effect Size - Cohen d:
## [1] 0.2706354
## Bayesian t-test Aligned (last block) compared to Rotation (last block):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.4208958 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Aligned (last block) compared to Mirror (last block):
##
## Paired t-test
##
## data: ALdat$compensation and MIRdatlast$compensation
## t = 0.82174, df = 15, p-value = 0.4241
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
## -16.61373 37.46155
## sample estimates:
## mean difference
## 10.42391
##
## Effect Size - Cohen d:
## [1] 0.2072793
## Bayesian t-test Aligned (last block) compared to Mirror (last block):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.3836858 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZSCOontrary to our findings with noninstructed participants, we found no effects for movement times across the different trial types for instructed participants.
We also compared MTs between rotation and mirror reversed reaches across training trials.
movementtimePerturbANOVA(group='instructed')## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 perturbtype 1 14 2.903503 0.110470854 0.011733371
## 3 block 2 28 8.888595 0.001025946 * 0.036601364
## 4 perturbtype:block 2 28 2.440166 0.105464379 0.007507154
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.4914825 0.009881032 *
## 4 perturbtype:block 0.7713684 0.185012880
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 block 0.6629025 0.004702904 * 0.7056493 0.003871487
## 4 perturbtype:block 0.8139136 0.118010748 0.9059609 0.111665143
## p[HF]<.05
## 3 *
## 4MTBayesANOVA(group='instructed')## Bayes factor analysis
## --------------
## [1] perturbtype + participant : 1.919917 ±25.93%
## [2] block + participant : 32.80978 ±0.59%
## [3] perturbtype + block + participant : 62.76471 ±1.84%
## [4] perturbtype + block + perturbtype:block + participant : 31.73064 ±1.94%
##
## Against denominator:
## compensation ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## perturbtype 0.60 0.74 1.90
## block 0.60 0.98 29.07
## block:perturbtype 0.20 0.24 1.29
##
## * Compared among: all models
## * Priors odds: uniform-equalWe find a main effect of block.
MTPerturbComparisonsAllBlocksEffSize(group='instructed')## contrast estimate SE df t.ratio p.value
## Block1: MIR vs. Block2: MIR 16.70 10.84 14 1.541 1.0000
## Block1: MIR vs. Block3: MIR 35.17 12.21 14 2.879 0.0849
## Block1: ROT vs. Block2: ROT 11.29 3.46 14 3.263 0.0397
## Block1: ROT vs. Block3: ROT 13.99 4.73 14 2.960 0.0723
## Block1: ROT vs. MIR 20.12 11.61 14 1.733 0.7350
## Block2: ROT vs. MIR 14.71 7.70 14 1.911 0.5369
## Block3: ROT vs. MIR -1.06 6.01 14 -0.176 1.0000
##
## P value adjustment: bonferroni method for 7 tests
## contrast etasquared
## 1 Block1: MIR vs. Block2: MIR 0.144995137
## 2 Block1: MIR vs. Block3: MIR 0.371955088
## 3 Block1: ROT vs. Block2: ROT 0.431948009
## 4 Block1: ROT vs. Block3: ROT 0.384990870
## 5 Block1: ROT vs. MIR 0.176677482
## 6 Block2: ROT vs. MIR 0.206885078
## 7 Block3: ROT vs. MIR 0.002214905MTBayesfollowup(group='instructed')## Bayesian t-test Mirror block 1 vs block 2:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.4414337 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test Mirror block 1 vs last block:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.9671488 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test Rotation block 1 vs block 2:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.3902021 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test Rotation block 1 vs last block:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.4216524 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test Rotation block 1 vs Mirror block 1:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.4735159 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test Rotation block 2 vs Mirror block 2:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.4406352 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test Rotation last block vs Mirror last block:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.344796 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZSFollow up tests show that the block effect is driven by changes within rotation MTs across blocks of trials. However, this is not supported with Bayesian tests. Thus, there are no differences in MTs between the two perturbation types.
Path length
We defined path length (PL) as the total distance, given x and y coordinates of the reach trajectory, traveled between movement onset and offset. Movement onset and offset are the start and end movement times defined in the previous section. The shortest path length to the target is a straight line spanning the start-to-target distance. However, movements are not perfectly straight and may travel in different directions, depending on the perturbation.
plotPTypePathLength(group='instructed')
Interestingly, we find that there is less PL variability in mirror reversed reaches for instructed participants compared to those observed with noninstructed participants. This suggests that they used the instructions to move in an optimal manner towards the target. Similar to the other measures above, we conducted t-tests to compare PLs between the last block of aligned trials with the first and last blocks of rotation and mirror reversed training. We then compared PLs between the two perturbation types.
PLt.test(group='instructed')## Aligned (last block) compared to Rotation (first block):
##
## Paired t-test
##
## data: ALdat$compensation and ROTdat$compensation
## t = 0.49754, df = 15, p-value = 0.626
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
## -0.1035788 0.1666597
## sample estimates:
## mean difference
## 0.03154043
##
## Effect Size - Cohen d:
## [1] 0.1643365
## Bayesian t-test Aligned (last block) compared to Rotation (first block):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.365352 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Aligned (last block) compared to Mirror (first block):
##
## Paired t-test
##
## data: ALdat$compensation and MIRdat$compensation
## t = -1.3083, df = 15, p-value = 0.2104
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
## -0.25508971 0.06103991
## sample estimates:
## mean difference
## -0.0970249
##
## Effect Size - Cohen d:
## [1] 0.4543367
## Bayesian t-test Aligned (last block) compared to Mirror (first block):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.6291118 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Aligned (last block) compared to Rotation (last block):
##
## Paired t-test
##
## data: ALdat$compensation and ROTdatlast$compensation
## t = 1.4415, df = 15, p-value = 0.17
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
## -0.05628912 0.29152108
## sample estimates:
## mean difference
## 0.117616
##
## Effect Size - Cohen d:
## [1] 0.5095843
## Bayesian t-test Aligned (last block) compared to Rotation (last block):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.7370795 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Aligned (last block) compared to Mirror (last block):
##
## Paired t-test
##
## data: ALdat$compensation and MIRdatlast$compensation
## t = 1.1824, df = 15, p-value = 0.2555
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
## -0.07107669 0.24817718
## sample estimates:
## mean difference
## 0.08855025
##
## Effect Size - Cohen d:
## [1] 0.3965926
## Bayesian t-test Aligned (last block) compared to Mirror (last block):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.5429388 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZSpathlengthPerturbANOVA(group='instructed')## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 perturbtype 1 15 4.059351 0.062216098 0.06247162
## 3 block 2 30 1.888061 0.168916472 0.04353613
## 4 perturbtype:block 2 30 6.702051 0.003925159 * 0.02868146
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.9524859 0.71122989
## 4 perturbtype:block 0.6704794 0.06091134
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 block 0.9546411 0.171121690 1.0904106 0.168916472
## 4 perturbtype:block 0.7521508 0.008875787 * 0.8176245 0.007147874
## p[HF]<.05
## 3
## 4 *PLBayesANOVA(group='instructed')## Bayes factor analysis
## --------------
## [1] perturbtype + participant : 5.01356 ±1.13%
## [2] block + participant : 0.6411715 ±0.84%
## [3] perturbtype + block + participant : 3.719959 ±3.13%
## [4] perturbtype + block + perturbtype:block + participant : 2.00664 ±3.07%
##
## Against denominator:
## compensation ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## perturbtype 0.60 0.87 4.36
## block 0.60 0.51 0.706
## block:perturbtype 0.20 0.16 0.774
##
## * Compared among: all models
## * Priors odds: uniform-equalWe find a significant perturbation type by block interaction, but only in the frequentist test.
PLPerturbComparisonsAllBlocksEffSize(group='instructed')## contrast estimate SE df t.ratio p.value
## Block1: MIR vs. Block2: MIR -0.0128 0.0692 15 -0.185 1.0000
## Block1: MIR vs. Block3: MIR 0.1856 0.0790 15 2.350 0.2300
## Block1: ROT vs. Block2: ROT 0.1092 0.0898 15 1.216 1.0000
## Block1: ROT vs. Block3: ROT 0.0861 0.0754 15 1.142 1.0000
## Block1: ROT vs. MIR 0.1286 0.0714 15 1.801 0.6432
## Block2: ROT vs. MIR 0.2505 0.0828 15 3.024 0.0598
## Block3: ROT vs. MIR 0.0291 0.0734 15 0.396 1.0000
##
## P value adjustment: bonferroni method for 7 tests
## contrast etasquared
## 1 Block1: MIR vs. Block2: MIR 0.002278355
## 2 Block1: MIR vs. Block3: MIR 0.269141772
## 3 Block1: ROT vs. Block2: ROT 0.089723709
## 4 Block1: ROT vs. Block3: ROT 0.079968756
## 5 Block1: ROT vs. MIR 0.177749702
## 6 Block2: ROT vs. MIR 0.378812974
## 7 Block3: ROT vs. MIR 0.010335440Following up on the frequentist test does not reveal any effects. Thus, we conclude that path lengths do not differ across trial types and between perturbation types.
Study 2: Online experiment results
The online experiment consisted of two sessions. In the first session, participants (N = 63) trained with the mirror reversal perturbation in a browser-based task, while using their dominant hand to control either their mouse or trackpad. They then returned for a second session (N = 48), where they immediately had to complete the same mirror reversed reaches, so that we may test for retention. We then tested for generalization by having participants complete mirror reversed reaches to different target locations across the workspace, and with their untrained/ non-dominant hand.
Target locations were either 5 degrees, 45 degrees, or 85 degrees away from a mirror axis placed along the vertical midline. We refer to these as near, middle, and far targets respectively.
Session 1
The first session began with 45 trials of aligned reaches with the participants’ dominant hand. Then they switched to using their non-dominant hand to complete 21 trials of aligned reaches. We then instructed them to switch back to using their dominant hand to complete 90 mirror reversed trials. Finally, they completed 21 trials of washout trials using their trained/ dominant hand.
Learning
We observe really fast learning in the online paradigm (see also supplementary R notebook), which is due to participants exploring the workspace during the very first trial. Regardless, participants learned to compensate for the mirror reversal in each of the target locations accordingly.
plotBlockedMirCtrl()
Before comparing learning across the three target locations, we first tested whether reaching performance in aligned reaches differed depending on the hand used to control the cursor. Thus we took the aligned reaches from each hand, and compared the first, second, and last block of reaching trials (trials 1-9, 10-18, 37-45 for the dominant hand, trials 46-48, 49-51, 64-66 for the nondominant hand) to the three target locations. We conducted a 3x3x2 (target x block x hand) within-subjects ANOVA.
alignedLearningANOVA2Hands()## Comparing targets and blocks between trained and untrained hands:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 target 2 124 0.2179356 0.8044846 0.0004305633
## 3 block 2 124 1.3531164 0.2622224 0.0024565576
## 4 hand 1 62 1.9838470 0.1639809 0.0026447799
## 5 target:block 4 248 1.2672615 0.2834110 0.0043808665
## 6 target:hand 2 124 1.9789967 0.1425491 0.0039777107
## 7 block:hand 2 124 1.3071810 0.2742839 0.0015969121
## 8 target:block:hand 4 248 0.7323503 0.5706330 0.0023947652
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 2 target 0.9897920 0.7312906822
## 3 block 0.9037101 0.0455920517 *
## 5 target:block 0.5974755 0.0002844163 *
## 6 target:hand 0.9901295 0.7389344283
## 7 block:hand 0.9614900 0.3018665755
## 8 target:block:hand 0.7066081 0.0127693436 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF] p[HF]<.05
## 2 target 0.9898951 0.8022947 1.0223789 0.8044846
## 3 block 0.9121675 0.2618553 0.9383619 0.2620144
## 5 target:block 0.8270634 0.2862176 0.8792547 0.2855044
## 6 target:hand 0.9902260 0.1430381 1.0227374 0.1425491
## 7 block:hand 0.9629180 0.2739438 0.9931696 0.2742274
## 8 target:block:hand 0.8525704 0.5501990 0.9082129 0.5582730alignedLearning2HandsBayesANOVA()## Bayes factor analysis
## --------------
## [1] target + participant : 0.01284371 ±0.65%
## [2] block + participant : 0.04112411 ±1.69%
## [3] target + block + participant : 0.0005128466 ±0.97%
## [4] target + block + target:block + participant : 1.126189e-05 ±1.75%
## [5] hand + participant : 0.2960377 ±1.25%
## [6] target + hand + participant : 0.003818392 ±1.52%
## [7] block + hand + participant : 0.01202038 ±2.04%
## [8] target + block + hand + participant : 0.0001504951 ±1.77%
## [9] target + block + target:block + hand + participant : 3.360743e-06 ±2.08%
## [10] target + hand + target:hand + participant : 0.0006865578 ±3.38%
## [11] target + block + hand + target:hand + participant : 2.736191e-05 ±2.51%
## [12] target + block + target:block + hand + target:hand + participant : 5.998548e-07 ±2.47%
## [13] block + hand + block:hand + participant : 0.0005548486 ±1.73%
## [14] target + block + hand + block:hand + participant : 7.3175e-06 ±2.18%
## [15] target + block + target:block + hand + block:hand + participant : 1.599796e-07 ±2.19%
## [16] target + block + hand + target:hand + block:hand + participant : 1.262937e-06 ±2.38%
## [17] target + block + target:block + hand + target:hand + block:hand + participant : 3.866889e-08 ±26.44%
## [18] target + block + target:block + hand + target:hand + block:hand + target:block:hand + participant : 6.768554e-10 ±3.76%
##
## Against denominator:
## angdev ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 0.01 0.005
## block 0.74 0.04 0.015
## block:target 0.32 1.13e-05 2.44e-05
## hand 0.74 0.23 0.106
## hand:target 0.32 5.23e-04 0.001
## block:hand 0.32 4.12e-04 8.93e-04
## block:hand:target 0.05 4.95e-10 8.91e-09
##
## * Compared among: all models
## * Priors odds: uniform-equalWe do not find an effect for the hand used, suggesting that aligned reaching performance is not different regardless of which hand was used.
Next, given that we observe fast learning, we cannot fit the exponential function to this data and generate reliable measures of learning rate and learning asymptote. Instead, we compare reaching performance to the three target locations across the first, second, and last few blocks of training trials (trials 1-3, 4-6, 76-90). We conduct a 3x3 (target x block) within-subjects ANOVA. We converted the angular reach deviations to percentage of compensation, such that the three target locations will be comparable.
mirrorANOVA()## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 target 2 124 3.0295259 0.0519312 0.008910013
## 3 block 2 124 0.3898554 0.6779818 0.001475398
## 4 target:block 4 248 0.7498522 0.5589303 0.005797917
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 2 target 0.081089137 5.288856e-34 *
## 3 block 0.788174290 7.030384e-04 *
## 4 target:block 0.001314326 1.719368e-80 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF] p[HF]<.05
## 2 target 0.5211289 0.08499643 0.5221834 0.0849105
## 3 block 0.8252012 0.63813105 0.8448718 0.6430256
## 4 target:block 0.4217775 0.45392147 0.4322788 0.4569101mirrorBayesANOVA()## Bayes factor analysis
## --------------
## [1] target + participant : 0.2386455 ±1.1%
## [2] block + participant : 0.02992001 ±1.59%
## [3] target + block + participant : 0.007144021 ±1.64%
## [4] target + block + target:block + participant : 0.0002117232 ±2.08%
##
## Against denominator:
## percentcomp ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.60 0.19 0.159
## block 0.60 0.03 0.020
## block:target 0.20 1.66e-04 6.64e-04
##
## * Compared among: all models
## * Priors odds: uniform-equalWe do not find any effects, suggesting that reaching performance did not differ across the the three target locations throughout training.
Reach aftereffects
From the plot, we do not observe evidence of reach aftereffects in all targets. To quantify this, we compared the first two blocks of trials during washout (trials 1-3, 4-6) with aligned reaches to the three targets. We conducted a 3x3 (block x target) within-subjects ANOVA.
RAETrainedTargetsANOVA()## Comparing angular reach deviations during washout trials with aligned trials across targets and blocks, trained hand:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 block 2 124 5.5489808 0.004919479 * 0.0188621974
## 3 target 2 124 0.2323375 0.793022859 0.0009205765
## 4 block:target 4 248 0.5536739 0.696516136 0.0037747082
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 2 block 0.8438785 5.643359e-03 *
## 3 target 0.9432319 1.682147e-01
## 4 block:target 0.5573588 5.277465e-05 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF] p[HF]<.05
## 2 block 0.8649610 0.007331719 * 0.8875473 0.00685751 *
## 3 target 0.9462814 0.780948587 0.9751826 0.78755341
## 4 block:target 0.8083289 0.659341405 0.8580494 0.66975796RAETrainedTargetsBayesANOVA()## Bayes factor analysis
## --------------
## [1] target + participant : 0.02529641 ±0.62%
## [2] block + participant : 4.271815 ±1.73%
## [3] target + block + participant : 0.1067235 ±1.24%
## [4] target + block + target:block + participant : 0.002025959 ±1.7%
##
## Against denominator:
## angdev ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.60 0.02 0.017
## block 0.60 0.81 2.85
## block:target 0.20 3.75e-04 0.001
##
## * Compared among: all models
## * Priors odds: uniform-equalWe find a main effect of block.
RAETrainedTargetsComparisonsEffSize()## contrast estimate SE df t.ratio p.value
## Aligned vs. Washout_b1 11.81 3.25 62 3.639 0.0017
## Aligned vs. Washout_b2 8.47 3.30 62 2.564 0.0384
## Washout_b1 vs. Washout_b2 -3.34 4.32 62 -0.775 1.0000
##
## P value adjustment: bonferroni method for 3 tests
## contrast etasquared
## 1 Aligned vs. Washout_b1 0.17599701
## 2 Aligned vs. Washout_b2 0.09585021
## 3 Washout_b1 vs. Washout_b2 0.00958323RAETrainedTargetsBayesfollowup()## Bayesian t-test aligned vs washout block 1:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 87.01229 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test aligned vs washout block 2:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 3.095192 ±0.01%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test washout block 1 vs washout block 2:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.2464351 ±0.03%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZSFollow up tests show that the aligned session differs from both first and second washout blocks, suggesting that aftereffects are present.
RAETrainedTargetsComparisonMeans()## block emmean SE df lower.CL upper.CL
## baseline -3.14 0.975 62 -5.09 -1.2
## first 8.66 3.003 62 2.66 14.7
## second 5.32 3.246 62 -1.17 11.8
##
## Confidence level used: 0.95However, these aftereffects are minimal (means of ~8 and 5 degrees for first and second blocks, respectively). Moreover, angular reach deviations do not differ between the first and second blocks of washout, suggesting that no de-adaptation is occurring.
Movement analysis
We then repeated the same set of tests we conducted for learning and reach aftereffects, but with completion time and path length as the dependent variables.
Completion time
In the online study, the target for the next trial was shown as soon as the cursor acquired the start position. This meant that participants made movements towards the centre of the start position, before moving in the direction of the target again. As such, defining RTs would produce unreliable measures. We instead defined completion time, as the time elapsed between target onset and target acquisition (i.e., includes both RT plus MT).
plotCtrlMT()
We observe that completion time seems to be longer at the start of every trial type, and becomes faster as the trials progress. Therefore, in aligned reaches, we first test for an effect of target or block while participants used either their dominant or non-dominant hand. We conduct a 3x3 (target x block) within-subjects ANOVA for the dominant hand, and conduct the same test for aligned trials using the non-dominant hand.
alignedMTANOVA()## Movement time during aligned trials across targets and blocks, trained hand:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 block 2 124 13.9833711 3.339906e-06 * 0.0184311123
## 3 target 2 124 3.7807763 2.547693e-02 * 0.0039431677
## 4 block:target 4 248 0.4007115 8.080525e-01 0.0001096509
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 2 block 0.3091451 2.818061e-16 *
## 3 target 0.2870943 2.949510e-17 *
## 4 block:target 0.6247809 8.159855e-04 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 2 block 0.5914168 0.0001673766 * 0.5962010 0.0001598296
## 3 target 0.5838033 0.0494976243 * 0.5881670 0.0491594253
## 4 block:target 0.8200657 0.7701889579 0.8713278 0.7819377433
## p[HF]<.05
## 2 *
## 3 *
## 4
##
## Movement time during aligned trials across targets and blocks, untrained hand:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 block 2 124 6.2489955 0.00259607 * 0.0167569456
## 3 target 2 124 2.3304727 0.10149548 0.0018845990
## 4 block:target 4 248 0.2765287 0.89298574 0.0003957172
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 2 block 0.4381320 1.172062e-11 *
## 3 target 0.9836857 6.055076e-01
## 4 block:target 0.2761175 4.668220e-13 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF] p[HF]<.05
## 2 block 0.6402590 0.009194215 * 0.6478368 0.008951399 *
## 3 target 0.9839476 0.102436849 1.0159347 0.101495479
## 4 block:target 0.5910539 0.794635028 0.6160126 0.803213183alignedMTBayesANOVA()## Bayes factor analysis
## --------------
## [1] target + participant : 3.1435 ±0.6%
## [2] block + participant : 2075399750 ±0.73%
## [3] target + block + participant : 11596816376 ±1.45%
## [4] target + block + target:block + participant : 95971631 ±1.15%
##
## Against denominator:
## movementtime ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.60 0.85 3.76
## block 0.60 1.00 2.22e+09
## block:target 0.20 6.97e-03 0.028
##
## * Compared among: all models
## * Priors odds: uniform-equalBayes factor analysis
## --------------
## [1] target + participant : 0.0784763 ±0.85%
## [2] block + participant : 7225.742 ±0.54%
## [3] target + block + participant : 627.6455 ±1.53%
## [4] target + block + target:block + participant : 5.911973 ±1.52%
##
## Against denominator:
## movementtime ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.60 0.08 0.058
## block 0.60 1.00 4.86e+03
## block:target 0.20 7.52e-04 0.003
##
## * Compared among: all models
## * Priors odds: uniform-equalWe find main effects of target and block for the trained hand, and a main effect of block for the untrained hand. The effect of block is expected, given that completion time becomes faster as trials progress. We investigate the target effect in the trained hand further.
trainedHandMTComparisonsEffSizeTargetEffect()## contrast estimate SE df t.ratio p.value
## Far vs. Mid 0.0941 0.0278 62 3.378 0.0038
## Far vs. Near 0.1778 0.0818 62 2.173 0.1008
## Mid vs. Near 0.0837 0.0713 62 1.174 0.7346
##
## P value adjustment: bonferroni method for 3 tests
## contrast etasquared
## 1 Far vs. Mid 0.15542100
## 2 Far vs. Near 0.07077687
## 3 Mid vs. Near 0.02174738trainedHandMTTargetEffectBayesfollowup()## Bayesian t-test far vs mid target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.2229243 ±0.03%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test far vs near target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.2637326 ±0.03%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test mid vs near target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.2035166 ±0.04%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZSFollow up frequentist tests show that the target effect is driven by a difference between the far and middle target. However, this difference is small and does not hold up in Bayesian t-tests. This may suggest that perhaps movements towards the far target are faster to initiate and execute.
Since we have confirmed these patterns within each hand’s aligned trials, we then test for an effect of hand used in completion time with a 3x3x2 (target x block x hand) within-subjects ANOVA.
alignedMTANOVA2Hands()## Comparing targets and blocks between trained and untrained hands:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 target 2 124 3.1793455 4.502617e-02 * 1.902889e-03
## 3 block 2 124 10.9050773 4.338131e-05 * 1.738211e-02
## 4 hand 1 62 8.3774637 5.238065e-03 * 6.158510e-03
## 5 target:block 4 248 0.2066594 9.345755e-01 1.018792e-04
## 6 target:hand 2 124 2.7305726 6.910332e-02 8.437125e-04
## 7 block:hand 2 124 0.1433789 8.665692e-01 7.573291e-05
## 8 target:block:hand 4 248 0.3831093 8.206260e-01 1.746956e-04
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 2 target 0.6649390 3.934091e-06 *
## 3 block 0.2833814 1.983024e-17 *
## 5 target:block 0.2383686 8.055260e-15 *
## 6 target:hand 0.7857191 6.392243e-04 *
## 7 block:hand 0.6450537 1.558380e-06 *
## 8 target:block:hand 0.3877660 4.649175e-09 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 2 target 0.7490294 0.0601965745 0.7634276 0.0592095729
## 3 block 0.5825406 0.0008758157 * 0.5868350 0.0008489665
## 5 target:block 0.6141871 0.8554825790 0.6414461 0.8637610904
## 6 target:hand 0.8235327 0.0801469054 0.8430834 0.0788517477
## 7 block:hand 0.7380366 0.8016187696 0.7517078 0.8058280661
## 8 target:block:hand 0.6467472 0.7355183318 0.6773781 0.7448918107
## p[HF]<.05
## 2
## 3 *
## 5
## 6
## 7
## 8alignedMT2HandsBayesANOVA()## Bayes factor analysis
## --------------
## [1] target + participant : 0.2276879 ±1.35%
## [2] block + participant : 71097209000 ±1.74%
## [3] target + block + participant : 19014797885 ±1.56%
## [4] target + block + target:block + participant : 50498369 ±1.18%
## [5] hand + participant : 1952.703 ±1.36%
## [6] target + hand + participant : 464.2093 ±2.4%
## [7] block + hand + participant : 2.473523e+14 ±1.49%
## [8] target + block + hand + participant : 7.014321e+13 ±1.74%
## [9] target + block + target:block + hand + participant : 187211786729 ±2.57%
## [10] target + hand + target:hand + participant : 36.92647 ±3.62%
## [11] target + block + hand + target:hand + participant : 5.865406e+12 ±2.44%
## [12] target + block + target:block + hand + target:hand + participant : 16207032451 ±2.69%
## [13] block + hand + block:hand + participant : 5.563654e+12 ±1.71%
## [14] target + block + hand + block:hand + participant : 1.567277e+12 ±2.75%
## [15] target + block + target:block + hand + block:hand + participant : 4206213736 ±2.64%
## [16] target + block + hand + target:hand + block:hand + participant : 144390377958 ±8.39%
## [17] target + block + target:block + hand + target:hand + block:hand + participant : 358196950 ±2.73%
## [18] target + block + target:block + hand + target:hand + block:hand + target:block:hand + participant : 3319574 ±2.65%
##
## Against denominator:
## movementtime ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 0.24 0.110
## block 0.74 1.00 4.81e+10
## block:target 0.32 6.29e-04 0.001
## hand 0.74 1.00 1.31e+03
## hand:target 0.32 0.02 0.040
## block:hand 0.32 0.02 0.049
## block:hand:target 0.05 1.00e-08 1.81e-07
##
## * Compared among: all models
## * Priors odds: uniform-equalWe find a main effect of hand.
MTComparisonsHandEffect()##
## Paired t-test
##
## data: trained$movementtime and untrained$movementtime
## t = -2.8944, df = 62, p-value = 0.002619
## alternative hypothesis: true mean difference is less than 0
## 95 percent confidence interval:
## -Inf -0.08422589
## sample estimates:
## mean difference
## -0.199074
##
## Bayesian t-test (trained hand vs. untrained hand):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 -Inf<d<0 : 321.9046 ±0%
##
## Against denominator:
## Alternative, r = 0.707106781186548, mu =/= 0 !(-Inf<d<0)
## ---
## Bayes factor type: BFoneSample, JZSFollow-up tests suggest that completion time in the trained (dominant) hand is faster than in the untrained (nondominant) hand.
Next, we conduct a 3x3 (target x block) within-subjects ANOVA to test for completion time effects during the mirror reversed trials.
mirrorMTANOVA()## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 target 2 124 24.240009 1.301187e-09 * 0.06931910
## 3 block 2 124 41.536873 1.557371e-14 * 0.13156353
## 4 target:block 4 248 3.768315 5.385664e-03 * 0.01756984
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 2 target 0.9744759 4.544840e-01
## 3 block 0.6582257 2.886900e-06 *
## 4 target:block 0.2727198 3.320161e-13 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 2 target 0.9751112 1.985595e-09 * 1.0063651 1.301187e-09
## 3 block 0.7452818 1.957267e-11 * 0.7594312 1.315793e-11
## 4 target:block 0.5725432 2.047303e-02 * 0.5957181 1.902400e-02
## p[HF]<.05
## 2 *
## 3 *
## 4 *mirrorMTBayesANOVA()## Bayes factor analysis
## --------------
## [1] target + participant : 7694467 ±0.71%
## [2] block + participant : 9.71082e+16 ±48.29%
## [3] target + block + participant : 1.702159e+25 ±1.27%
## [4] target + block + target:block + participant : 2.227982e+25 ±1.92%
##
## Against denominator:
## movementtime ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.60 1.00 2.70e+08
## block 0.60 1.00 3.41e+18
## block:target 0.20 0.57 5.24
##
## * Compared among: all models
## * Priors odds: uniform-equalWe find a significant block by target interaction.
mirrorMTComparisonsEffSize()## contrast estimate SE df t.ratio p.value
## 1st block: Far vs. Mid 3.77155 0.684 62 5.516 <.0001
## 1st block: Far vs. Near 1.35750 0.858 62 1.581 1.0000
## 1st block: Mid vs. Near -2.41405 1.024 62 -2.357 0.1942
## 2nd block: Far vs. Mid 2.91477 0.497 62 5.866 <.0001
## 2nd block: Far vs. Near 1.35358 0.497 62 2.725 0.0752
## 2nd block: Mid vs. Near -1.56119 0.538 62 -2.903 0.0460
## last block: Far vs. Mid 1.00064 0.149 62 6.709 <.0001
## last block: Far vs. Near 0.99615 0.152 62 6.543 <.0001
## last block: Mid vs. Near -0.00449 0.145 62 -0.031 1.0000
##
## P value adjustment: bonferroni method for 9 tests
## contrast etasquared
## 1 1st block: Far vs. Mid 3.291755e-01
## 2 1st block: Far vs. Near 3.876890e-02
## 3 1st block: Mid vs. Near 8.225596e-02
## 4 2nd block: Far vs. Mid 3.569403e-01
## 5 2nd block: Far vs. Near 1.069388e-01
## 6 2nd block: Mid vs. Near 1.196496e-01
## 7 last block: Far vs. Mid 4.206092e-01
## 8 last block: Far vs. Near 4.084704e-01
## 9 last block: Mid vs. Near 1.534659e-05mirrorMTBayesfollowup()## FIRST BLOCK:
## Bayesian t-test far vs mid target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 452.3834 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test far vs near target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.4475591 ±0.02%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test mid vs near target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 1.501172 ±0.01%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## SECOND BLOCK:
## Bayesian t-test far vs mid target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 12111.64 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test far vs near target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 3.664137 ±0.01%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test mid vs near target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 1.675191 ±0.01%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## LAST BLOCK:
## Bayesian t-test far vs mid target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 61409.25 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test far vs near target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 16874.16 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test mid vs near target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.1901957 ±0.04%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZSFollow-up tests show faster completion times for the far target compared to the middle target across all three blocks. The far target is also faster than the near target for the last block. These results suggest that movement initiation and execution towards the far target is faster than the other two targets.
For washout trials, we first conduct a 3x2 (target x first and second block) within-subject ANOVA, to test for any effects across target locations.
RAEMTANOVA()## Warning: You have removed one or more levels from variable "block". Refactoring
## for ANOVA.## Movement time during washout trials across targets and blocks, trained hand:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 block 1 62 49.1623291 2.053179e-09 * 0.0239235714
## 3 target 2 124 4.2110240 1.700614e-02 * 0.0068722931
## 4 block:target 2 124 0.1097604 8.961358e-01 0.0001621676
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 target 0.9978041 0.9351505
## 4 block:target 0.9377759 0.1409358
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF] p[HF]<.05
## 3 target 0.9978089 0.0170779 * 1.0309574 0.01700614 *
## 4 block:target 0.9414209 0.8851467 0.9699314 0.89064933RAEMTBayesANOVA()## Bayes factor analysis
## --------------
## [1] target + participant : 1.577128 ±0.99%
## [2] block + participant : 550030.9 ±6.68%
## [3] target + block + participant : 1281446 ±7.66%
## [4] target + block + target:block + participant : 68118.39 ±1.23%
##
## Against denominator:
## movementtime ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.60 0.71 1.64
## block 0.60 1.00 4.91e+05
## block:target 0.20 0.04 0.149
##
## * Compared among: all models
## * Priors odds: uniform-equalWe find main effects of target and block, but no interaction.
RAEMTComparisonsEffSizeTargetEffect()## contrast estimate SE df t.ratio p.value
## Far vs. Mid 0.0957 0.0509 62 1.879 0.1947
## Far vs. Near 0.1468 0.0506 62 2.901 0.0154
## Mid vs. Near 0.0511 0.0525 62 0.973 1.0000
##
## P value adjustment: bonferroni method for 3 tests
## contrast etasquared
## 1 Far vs. Mid 0.05389934
## 2 Far vs. Near 0.11950706
## 3 Mid vs. Near 0.01504785RAEMTTargetEffectBayesfollowup()## Bayesian t-test far vs mid target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.2486001 ±0.03%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test far vs near target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.3606759 ±0.03%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test mid vs near target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.2061641 ±0.04%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZSFollow-up tests show that the target effect is driven by a difference between the far and near targets, but these differences are small and do not hold up in Bayesian tests.
Now that we have confirmed these patterns, we can now compare washout trials with those in aligned to test for completion time effects between aligned and washout trials. We conduct a 3x3 (target x block) within-subjects ANOVA, where block considers the aligned trials, first, and second block of washout trials.
RAEMTTrainedTargetsANOVA()## Comparing movement times during washout trials with aligned trials across targets and blocks, trained hand:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 block 2 124 9.93029285 9.994277e-05 * 0.0140440457
## 3 target 2 124 9.07320678 2.101446e-04 * 0.0065829384
## 4 block:target 4 248 0.09110735 9.851931e-01 0.0001319642
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 2 block 0.6351112 9.703270e-07 *
## 3 target 0.9718037 4.179711e-01
## 4 block:target 0.3307473 6.467021e-11 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 2 block 0.7326604 0.0005554876 * 0.7459791 0.0005097983
## 3 target 0.9725770 0.0002458168 * 1.0036217 0.0002101446
## 4 block:target 0.6347400 0.9470049475 0.6641091 0.9523221858
## p[HF]<.05
## 2 *
## 3 *
## 4RAEMTTrainedTargetsBayesANOVA()## Bayes factor analysis
## --------------
## [1] target + participant : 13.90487 ±1.15%
## [2] block + participant : 34690.49 ±0.91%
## [3] target + block + participant : 717509.8 ±2.21%
## [4] target + block + target:block + participant : 5905.53 ±1.93%
##
## Against denominator:
## movementtime ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.60 0.95 13.90
## block 0.60 1.00 3.39e+04
## block:target 0.20 7.79e-03 0.031
##
## * Compared among: all models
## * Priors odds: uniform-equalWe find main effects of block and target, but no interaction. We then conduct follow-up tests on the block effect, regardless of target location.
RAEMTTrainedTargetsComparisonsEffSize()## contrast estimate SE df t.ratio p.value
## Aligned vs. Washout_b1 0.0876 0.0598 62 1.466 0.4428
## Aligned vs. Washout_b2 -0.1414 0.0586 62 -2.414 0.0562
## Washout_b1 vs. Washout_b2 -0.2291 0.0327 62 -7.012 <.0001
##
## P value adjustment: bonferroni method for 3 tests
## contrast etasquared
## 1 Aligned vs. Washout_b1 0.0335211
## 2 Aligned vs. Washout_b2 0.0859177
## 3 Washout_b1 vs. Washout_b2 0.4422571RAEMTTrainedTargetsBlockEffectBayesfollowup()## Bayesian t-test aligned vs washout block 1:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.2259262 ±0.03%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test aligned vs washout block 2:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.3130464 ±0.03%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test washout block 1 vs washout block 2:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 1.036413 ±0.01%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZSWe find that the main effect of block is driven by a difference between the two blocks during washout, given that completion time is faster as trials progress. Overall, despite observing very small aftereffects, completion time during washout trials do not differ from completion times during aligned reaches.
Path length
We repeat the same set of analyses for completion time, with path lengths. We defined path lengths similar to how we defined it for the tablet study. In the online study, the shortest path from start to target is 0.4 height units (scaled to participant monitor size).
plotCtrlPL()
For aligned reaches, we first test for an effect of target or block while participants used either their dominant or non-dominant hand. We conduct a 3x3 (target x block) within-subjects ANOVA for the dominant hand, and conduct the same test for aligned trials using the non-dominant hand.
alignedPLANOVA()## Path length during aligned trials across targets and blocks, trained hand:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 block 2 124 0.70283794 0.4971397670 1.762978e-03
## 3 target 2 124 8.92708745 0.0002387442 * 1.862129e-02
## 4 block:target 4 248 0.02574106 0.9987097892 8.024887e-05
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 2 block 0.8325765 0.003740557 *
## 3 target 0.9735067 0.440897694
## 4 block:target 0.7160316 0.016867491 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF] p[HF]<.05
## 2 block 0.8565872 0.4765470227 0.878550 0.4799124260
## 3 target 0.9741905 0.0002758861 * 1.005368 0.0002387442 *
## 4 block:target 0.8696230 0.9972379563 0.927629 0.9980333414
##
## Path length during aligned trials across targets and blocks, untrained hand:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 block 2 124 5.6321301 0.004558214 * 0.014098260
## 3 target 2 124 0.8258100 0.440273720 0.002335364
## 4 block:target 4 248 0.8487599 0.495490318 0.004837177
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 2 block 0.9511044 0.2167500984
## 3 target 0.8534467 0.0079593914 *
## 4 block:target 0.6140091 0.0005428905 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF] p[HF]<.05
## 2 block 0.9533837 0.00524604 * 0.9828590 0.004799835 *
## 3 target 0.8721792 0.42620025 0.8953069 0.428906995
## 4 block:target 0.7953358 0.47432013 0.8433745 0.479759731alignedPLBayesANOVA()## Bayes factor analysis
## --------------
## [1] target + participant : 203.213 ±0.9%
## [2] block + participant : 0.04625301 ±1.16%
## [3] target + block + participant : 9.636059 ±1.19%
## [4] target + block + target:block + participant : 0.07444509 ±2.03%
##
## Against denominator:
## pathlength ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.60 1.00 135.67
## block 0.60 0.05 0.032
## block:target 0.20 3.48e-04 0.001
##
## * Compared among: all models
## * Priors odds: uniform-equalBayes factor analysis
## --------------
## [1] target + participant : 0.04318347 ±0.59%
## [2] block + participant : 2.603808 ±0.83%
## [3] target + block + participant : 0.1185538 ±1.6%
## [4] target + block + target:block + participant : 0.003646972 ±1.55%
##
## Against denominator:
## pathlength ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.60 0.04 0.031
## block 0.60 0.72 1.74
## block:target 0.20 9.68e-04 0.004
##
## * Compared among: all models
## * Priors odds: uniform-equalWe find a main effect of target for the trained hand, and a main effect of block for the untrained hand. From the plot, we observe that the path lengths become shorter as aligned reaches progress with the untrained/nondominant hand. Thus, we conduct follow up tests for the main effect of target in the trained hand.
trainedHandPLComparisonsEffSizeTargetEffect()## contrast estimate SE df t.ratio p.value
## Far vs. Mid 0.01020 0.00418 62 2.441 0.0526
## Far vs. Near -0.00689 0.00373 62 -1.847 0.2087
## Mid vs. Near -0.01709 0.00428 62 -3.994 0.0005
##
## P value adjustment: bonferroni method for 3 tests
## contrast etasquared
## 1 Far vs. Mid 0.08765434
## 2 Far vs. Near 0.05213559
## 3 Mid vs. Near 0.20466801trainedHandPLTargetEffectBayesfollowup()## Bayesian t-test far vs mid target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.3993048 ±0.02%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test far vs near target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.3074171 ±0.03%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test mid vs near target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 2.019948 ±0.01%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZSThe target effect is driven by a difference between middle and near target path lengths.
Next, we can compare the two aligned trials between the trained and untrained hands. We conduct a 3x3x2 (target x block x hand) within-subjects ANOVA.
alignedPLANOVA2Hands()## Comparing targets and blocks between trained and untrained hands:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 target 2 124 0.9370209 3.945495e-01 0.001410317
## 3 block 2 124 3.7850569 2.537435e-02 * 0.004789706
## 4 hand 1 62 32.4894316 3.555892e-07 * 0.046169631
## 5 target:block 4 248 0.8423108 4.994801e-01 0.002308271
## 6 target:hand 2 124 2.3006869 1.044520e-01 0.002855826
## 7 block:hand 2 124 6.3497149 2.369239e-03 * 0.007964748
## 8 target:block:hand 4 248 0.7438230 5.629464e-01 0.001986878
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 2 target 0.9230495 0.086968632
## 3 block 0.9607552 0.294909497
## 5 target:block 0.6420409 0.001533283 *
## 6 target:hand 0.8314675 0.003591538 *
## 7 block:hand 0.9117231 0.059678859
## 8 target:block:hand 0.6499961 0.002031332 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 2 target 0.9285478 0.388839776 0.9560315 0.391099567
## 3 block 0.9622372 0.026958635 * 0.9924332 0.025684081
## 5 target:block 0.8107457 0.479678184 0.8607819 0.485342045
## 6 target:hand 0.8557742 0.113058031 0.8776768 0.111725021
## 7 block:hand 0.9188838 0.003167035 * 0.9456045 0.002878002
## 8 target:block:hand 0.8120525 0.537031797 0.8622598 0.544467437
## p[HF]<.05
## 2
## 3 *
## 5
## 6
## 7 *
## 8alignedPL2HandsBayesANOVA()## Bayes factor analysis
## --------------
## [1] target + participant : 0.02473342 ±0.89%
## [2] block + participant : 0.2122014 ±0.77%
## [3] target + block + participant : 0.005724372 ±6.27%
## [4] target + block + target:block + participant : 4.766053e-05 ±2.34%
## [5] hand + participant : 5.366678e+12 ±0.81%
## [6] target + hand + participant : 141765455838 ±1.35%
## [7] block + hand + participant : 1.417406e+12 ±2%
## [8] target + block + hand + participant : 38623340424 ±2.97%
## [9] target + block + target:block + hand + participant : 358358310 ±2.71%
## [10] target + hand + target:hand + participant : 18826698560 ±1.76%
## [11] target + block + hand + target:hand + participant : 5038792506 ±4.68%
## [12] target + block + target:block + hand + target:hand + participant : 47475792 ±3.66%
## [13] block + hand + block:hand + participant : 7.786853e+12 ±29.9%
## [14] target + block + hand + block:hand + participant : 150040134921 ±2.57%
## [15] target + block + target:block + hand + block:hand + participant : 1428265209 ±1.99%
## [16] target + block + hand + target:hand + block:hand + participant : 19408823865 ±2.14%
## [17] target + block + target:block + hand + target:hand + block:hand + participant : 188364604 ±3.12%
## [18] target + block + target:block + hand + target:hand + block:hand + target:block:hand + participant : 4282461 ±3.08%
##
## Against denominator:
## pathlength ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 0.03 0.009
## block 0.74 0.63 0.609
## block:target 0.32 1.36e-04 2.94e-04
## hand 0.74 1.00 4.30e+12
## hand:target 0.32 2.91e-03 0.006
## block:hand 0.32 0.53 2.47
## block:hand:target 0.05 2.87e-07 5.16e-06
##
## * Compared among: all models
## * Priors odds: uniform-equalWe find a main effect of hand.
PLComparisonsHandEffect()##
## Paired t-test
##
## data: trained$pathlength and untrained$pathlength
## t = -5.7, df = 62, p-value = 1.778e-07
## alternative hypothesis: true mean difference is less than 0
## 95 percent confidence interval:
## -Inf -0.03286534
## sample estimates:
## mean difference
## -0.04648238
##
## Bayesian t-test (trained hand vs. untrained hand):## t is large; approximation invoked.
## t is large; approximation invoked.## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 -Inf<d<0 : 5624467 ±NA%
##
## Against denominator:
## Alternative, r = 0.707106781186548, mu =/= 0 !(-Inf<d<0)
## ---
## Bayes factor type: BFoneSample, JZSFollow-up tests comparing PLs in the two hands suggest that path lengths were longer for the untrained/ nondominant hand.
We then conducted a 3x3 (target x block) within-subjects ANOVA for path lengths during the mirror reversed trials.
mirrorPLANOVA()## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 target 2 124 22.848207 3.568117e-09 * 0.06955679
## 3 block 2 124 30.872062 1.316465e-11 * 0.12362195
## 4 target:block 4 248 4.766978 1.010407e-03 * 0.02462987
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 2 target 0.9997251 9.916481e-01
## 3 block 0.4613638 5.666666e-11 *
## 4 target:block 0.1788990 2.617593e-18 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 2 target 0.9997251 3.583854e-09 * 1.0330353 3.568117e-09
## 3 block 0.6499262 2.422326e-08 * 0.6580767 2.032174e-08
## 4 target:block 0.6458999 5.127498e-03 * 0.6764410 4.450701e-03
## p[HF]<.05
## 2 *
## 3 *
## 4 *mirrorPLBayesANOVA()## Bayes factor analysis
## --------------
## [1] target + participant : 1628909 ±0.78%
## [2] block + participant : 6.833028e+13 ±0.87%
## [3] target + block + participant : 1.734864e+21 ±0.98%
## [4] target + block + target:block + participant : 8.578155e+21 ±1.54%
##
## Against denominator:
## pathlength ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.60 1.00 1.01e+08
## block 0.60 1.00 4.22e+15
## block:target 0.20 0.83 19.78
##
## * Compared among: all models
## * Priors odds: uniform-equalWe find a significant target by block interaction.
mirrorPLComparisonsEffSize()## contrast estimate SE df t.ratio p.value
## 1st block: Far vs. Mid 0.9583 0.2424 62 3.953 0.0018
## 1st block: Far vs. Near 0.0138 0.2769 62 0.050 1.0000
## 1st block: Mid vs. Near -0.9444 0.2629 62 -3.592 0.0058
## 2nd block: Far vs. Mid 0.7965 0.1385 62 5.751 <.0001
## 2nd block: Far vs. Near 0.1987 0.0759 62 2.616 0.1003
## 2nd block: Mid vs. Near -0.5978 0.1319 62 -4.532 0.0002
## last block: Far vs. Mid 0.2245 0.0249 62 9.002 <.0001
## last block: Far vs. Near 0.1889 0.0428 62 4.409 0.0004
## last block: Mid vs. Near -0.0356 0.0398 62 -0.895 1.0000
##
## P value adjustment: bonferroni method for 9 tests
## contrast etasquared
## 1 1st block: Far vs. Mid 2.013354e-01
## 2 1st block: Far vs. Near 4.009271e-05
## 3 1st block: Mid vs. Near 1.722531e-01
## 4 2nd block: Far vs. Mid 3.478839e-01
## 5 2nd block: Far vs. Near 9.943038e-02
## 6 2nd block: Mid vs. Near 2.487997e-01
## 7 last block: Far vs. Mid 5.665241e-01
## 8 last block: Far vs. Near 2.387150e-01
## 9 last block: Mid vs. Near 1.276537e-02mirrorPLBayesfollowup()## FIRST BLOCK:
## Bayesian t-test far vs mid target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 7.73993 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test far vs near target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.190372 ±0.04%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test mid vs near target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 57.25084 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## SECOND BLOCK:
## Bayesian t-test far vs mid target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 135502.4 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test far vs near target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 2.951918 ±0.01%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test mid vs near target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 201.0545 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## LAST BLOCK:
## Bayesian t-test far vs mid target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 47194.94 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test far vs near target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 82.8316 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test mid vs near target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.2281068 ±0.03%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZSFollow-up tests show that the far target had shorter path lengths than the middle target across block of trials. The far target also had a shorter path length than the near target during the end of learning. Finally, the near target had shorter path lengths that the middle target for the first two blocks. Taken together, these results suggest that path lengths were shortest for the far target, and longest for the middle target.
For washout trials, we first conduct a 3x2 (target x first and second block) within-subjects ANOVA to investigate effects across target locations.
RAEPLANOVA()## Warning: You have removed one or more levels from variable "block". Refactoring
## for ANOVA.## Path length during washout trials across targets and blocks, trained hand:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 block 1 62 7.8792237 0.006675277 * 0.018132704
## 3 target 2 124 0.2796761 0.756504221 0.001280387
## 4 block:target 2 124 0.9761852 0.379621730 0.003187927
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 target 0.9416049 0.1595865
## 4 block:target 0.9713834 0.4124921
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF] p[HF]<.05
## 3 target 0.9448268 0.7440495 0.9736109 0.7506531
## 4 block:target 0.9721795 0.3777028 1.0031915 0.3796217RAEPLBayesANOVA()## Bayes factor analysis
## --------------
## [1] target + participant : 0.03770955 ±0.56%
## [2] block + participant : 8.798193 ±1.37%
## [3] target + block + participant : 0.3486831 ±1.91%
## [4] target + block + target:block + participant : 0.03660972 ±1.7%
##
## Against denominator:
## pathlength ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.60 0.04 0.029
## block 0.60 0.90 5.90
## block:target 0.20 3.58e-03 0.014
##
## * Compared among: all models
## * Priors odds: uniform-equalWe find a main effect of block, which is already evident from the plot.
Next, we conducted a 3x3 (target x block) within-subjects ANOVA, to test for target effects across the aligned trials, first and second blocks of washout trials.
RAEPLTrainedTargetsANOVA()## Comparing path length during washout trials with aligned trials across targets and blocks, trained hand:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 block 2 124 9.4553639 0.0001507041 * 0.031685134
## 3 target 2 124 0.6134957 0.5430899821 0.001977601
## 4 block:target 4 248 0.7343285 0.5693035410 0.003295324
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 2 block 0.5648765 2.720076e-08 *
## 3 target 0.9041194 4.622601e-02 *
## 4 block:target 0.3040437 6.547509e-12 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 2 block 0.6968041 0.0009424686 * 0.7078240 0.0008814147
## 3 target 0.9125082 0.5288205760 0.9387292 0.5332295422
## 4 block:target 0.7209152 0.5277716009 0.7598180 0.5343947151
## p[HF]<.05
## 2 *
## 3
## 4RAEPLTrainedTargetsBayesANOVA()## Bayes factor analysis
## --------------
## [1] target + participant : 0.03859411 ±1.9%
## [2] block + participant : 1212.457 ±0.7%
## [3] target + block + participant : 47.84131 ±3.26%
## [4] target + block + target:block + participant : 0.9354199 ±2.5%
##
## Against denominator:
## pathlength ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.60 0.04 0.027
## block 0.60 1.00 809.58
## block:target 0.20 7.41e-04 0.003
##
## * Compared among: all models
## * Priors odds: uniform-equalWe find a main effect of block.
RAEPLTrainedTargetsComparisonsEffSize()## contrast estimate SE df t.ratio p.value
## Aligned vs. Washout_b1 0.0533 0.0150 62 3.543 0.0023
## Aligned vs. Washout_b2 0.0127 0.0075 62 1.693 0.2866
## Washout_b1 vs. Washout_b2 -0.0406 0.0145 62 -2.807 0.0200
##
## P value adjustment: bonferroni method for 3 tests
## contrast etasquared
## 1 Aligned vs. Washout_b1 0.16834419
## 2 Aligned vs. Washout_b2 0.04417288
## 3 Washout_b1 vs. Washout_b2 0.11275488RAEPLTrainedTargetsBlockEffectBayesfollowup()## Bayesian t-test aligned vs washout block 1:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 10.49775 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test aligned vs washout block 2:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.3643568 ±0.03%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test washout block 1 vs washout block 2:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 1.413927 ±0.01%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZSHowever, follow-up tests show that the block effect is driven by the first block of washout trials having larger path lengths than in block 2 or aligned trials. This is likely due to switching from mirror reversed trials directly to washout trials. Overall, the path length results support results from the analysis with completion time.
Session 2
In session 2, we tested for retention and generalization across the workspace and hands. As such, the three possible target locations (far, middle, near) were positioned in either quadrant 1 (5°, 45°, or 85° in polar coordinates), quadrant 2 (95°, 135°, or 175° in polar coordinates), or quadrant 4 (275°, 315°, or 355° in polar coordinates), relative to the mirror axis along the vertical midline.
Participants returned on a different day, and immediately performed 21 trials of mirror reversed reaches to quadrant 1 targets using their dominant or trained hand. They then completed 21 trials of perturbed reaches to quadrant 4 targets followed by 21 trials to quadrant 2 targets. To prevent any possible decay in learning, we had them perform another 21 trials of perturbed reaches to quadrant 1 targets. Finally, we instructed them to switch to their non-dominant hand, and perform 21 trials of perturbed reaches to quadrant 1 targets. The session ended with participants completing 21 washout trials with their non-dominant/ untrained hand.
Performance for the three targets across quadrants
First, we plot a distribution for when participants returned for the second session.
plotCtrlDaysApart()
## mean: 4.77083333333333 days apart
## sd: 2.52004376298823 days apart
## median: 4 days apartMajority of participants returned after 3 to 4 days (mean = 4.77, SD = 2.52, median = 4 days apart), with a few returning after more than two weeks.
At the start of the session, we observe that participants are able to compensate for the mirror reversed perturbation quickly. This learned performance also seems to transfer well to the targets in other quadrants, as well as to the untrained hand.
plotBlockedLearningCtrlGen()
Learned performance
Before testing for retention and generalization, we first tested for target or block effects for reaches within each quadrant. Thus, we conducted 3x3 (target x block) within-subjects ANOVA for quadrants 1, 4, 2, top-up trials in quadrant 1 (Quadrant 1A in tests below), and quadrant 1 after switching hands (Quadrant 1L in tests below).
learningANOVA()## Quadrant 1:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 block 2 94 0.46901815 0.6270723 0.0023303901
## 3 target 2 94 1.24562325 0.2924671 0.0051810200
## 4 block:target 4 188 0.02043224 0.9991793 0.0001970206
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 2 block 0.996363137 9.196149e-01
## 3 target 0.090858412 1.102550e-24 *
## 4 block:target 0.003470507 4.926226e-50 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF] p[HF]<.05
## 2 block 0.9963763 0.6263803 1.0404116 0.6270723
## 3 target 0.5237956 0.2721925 0.5253738 0.2723274
## 4 block:target 0.5106443 0.9811571 0.5340814 0.9838602
##
## Quadrant 4:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 block 2 94 1.0757338 0.3452081283 0.005279960
## 3 target 2 94 8.2511489 0.0004995254 * 0.031337929
## 4 block:target 4 188 0.8965448 0.4671321323 0.008748321
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 2 block 0.762965018 1.984296e-03 *
## 3 target 0.101182361 1.310420e-23 *
## 4 block:target 0.002592564 8.119451e-53 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF] p[HF]<.05
## 2 block 0.8083846 0.334486154 0.8329610 0.33608568
## 3 target 0.5266435 0.005327945 * 0.5284141 0.00528064 *
## 4 block:target 0.4258706 0.397584997 0.4402499 0.40048576
##
## Quadrant 2:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 block 2 94 0.3680164 0.6930985 0.001578517
## 3 target 2 94 0.9332813 0.3968742 0.004704721
## 4 block:target 4 188 0.1199361 0.9752603 0.001058615
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 2 block 0.985079761 7.076885e-01
## 3 target 0.066513629 8.451714e-28 *
## 4 block:target 0.007941019 3.706517e-42 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF] p[HF]<.05
## 2 block 0.9852991 0.6899926 1.0280918 0.6930985
## 3 target 0.5172004 0.3419979 0.5183359 0.3421944
## 4 block:target 0.5160904 0.8928421 0.5401579 0.9008154
##
## Quadrant 1A:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 block 2 94 1.4773339 0.23349585 0.006861094
## 3 target 2 94 2.4410072 0.09257544 0.011487313
## 4 block:target 4 188 0.7199391 0.57928728 0.006442300
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 2 block 0.984293191 6.948052e-01
## 3 target 0.062014138 1.687665e-28 *
## 4 block:target 0.002802518 4.497067e-52 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF] p[HF]<.05
## 2 block 0.9845361 0.2337061 1.0272436 0.2334958
## 3 target 0.5159996 0.1239138 0.5170550 0.1238475
## 4 block:target 0.5064444 0.4910885 0.5293996 0.4967751
##
## Quadrant 1L:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 block 2 94 1.45681140 0.2381893 0.0056150199
## 3 target 2 94 0.08912497 0.9148085 0.0005084902
## 4 block:target 4 188 0.84565030 0.4978731 0.0067348165
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 2 block 0.925538099 1.686821e-01
## 3 target 0.068520083 1.674215e-27 *
## 4 block:target 0.002016678 3.234510e-55 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF] p[HF]<.05
## 2 block 0.9306984 0.2388813 0.9675427 0.2385421
## 3 target 0.5177377 0.7754530 0.5189091 0.7760227
## 4 block:target 0.4604347 0.4244841 0.4783369 0.4282104learningBayesANOVA()##
## Quadrant 1:
## Bayes factor analysis
## --------------
## [1] target + participant : 0.07807064 ±1.23%
## [2] block + participant : 0.04206727 ±0.86%
## [3] target + block + participant : 0.003191744 ±1.69%
## [4] target + block + target:block + participant : 3.723849e-05 ±1.34%
##
## Against denominator:
## percentcomp ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.60 0.07 0.052
## block 0.60 0.04 0.028
## block:target 0.20 3.31e-05 1.33e-04
##
## * Compared among: all models
## * Priors odds: uniform-equal
## Quadrant 4:
## Bayes factor analysis
## --------------
## [1] target + participant : 21.40354 ±1.4%
## [2] block + participant : 0.07631312 ±1.29%
## [3] target + block + participant : 1.718563 ±3.19%
## [4] target + block + target:block + participant : 0.08954715 ±1.77%
##
## Against denominator:
## percentcomp ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.60 0.96 14.38
## block 0.60 0.08 0.056
## block:target 0.20 3.69e-03 0.015
##
## * Compared among: all models
## * Priors odds: uniform-equal
## Quadrant 2:
## Bayes factor analysis
## --------------
## [1] target + participant : 0.07025134 ±0.71%
## [2] block + participant : 0.03636075 ±1.67%
## [3] target + block + participant : 0.002492599 ±1%
## [4] target + block + target:block + participant : 3.481845e-05 ±2%
##
## Against denominator:
## percentcomp ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.60 0.07 0.047
## block 0.60 0.04 0.024
## block:target 0.20 3.14e-05 1.26e-04
##
## * Compared among: all models
## * Priors odds: uniform-equal
## Quadrant 1A:
## Bayes factor analysis
## --------------
## [1] target + participant : 0.2948479 ±0.67%
## [2] block + participant : 0.1092902 ±1.37%
## [3] target + block + participant : 0.0325739 ±1.26%
## [4] target + block + target:block + participant : 0.001156858 ±1.43%
##
## Against denominator:
## percentcomp ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.60 0.23 0.197
## block 0.60 0.10 0.074
## block:target 0.20 8.05e-04 0.003
##
## * Compared among: all models
## * Priors odds: uniform-equal
## Quadrant 1L:
## Bayes factor analysis
## --------------
## [1] target + participant : 0.02871314 ±1.53%
## [2] block + participant : 0.08710613 ±0.77%
## [3] target + block + participant : 0.002527207 ±1.54%
## [4] target + block + target:block + participant : 0.0001023184 ±2.27%
##
## Against denominator:
## percentcomp ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.60 0.03 0.019
## block 0.60 0.08 0.058
## block:target 0.20 9.15e-05 3.66e-04
##
## * Compared among: all models
## * Priors odds: uniform-equalIn all tests, we only find a main effect of target for reaches in quadrant 4.
quadrant4ComparisonsEffSize()## contrast estimate SE df t.ratio p.value
## Far vs. Mid -15.2 7.12 47 -2.135 0.1139
## Far vs. Near 83.8 33.60 47 2.495 0.0485
## Mid vs. Near 99.0 29.81 47 3.322 0.0052
##
## P value adjustment: bonferroni method for 3 tests
## contrast etasquared
## 1 Far vs. Mid 0.08843739
## 2 Far vs. Near 0.11696547
## 3 Mid vs. Near 0.19013349quadrant4ComparisonsBayesfollowup()## Bayesian t-test far vs mid target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 1.465255 ±0.01%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test far vs near target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 3.465854 ±0.01%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test mid vs near target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 8.941381 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZSFollow-up tests show that the effect is driven by the difference between middle and near targets, regardless of block. This confirms what we observe in the plot above, where compensation percentages for the near target are easily overcompensated.
Retention
To quantify retention, we compare the learned performance between the last block of mirror reversed reaches in session 1, with the first block of mirror reversed reaches in session 2.
retentionANOVA()## Retention of learned performance, trained hand:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 target 2 94 0.08686344 0.9168758 0.0007296872
## 3 session 1 47 0.05827637 0.8102914 0.0001645907
## 4 target:session 2 94 0.56768055 0.5687697 0.0029940606
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 2 target 0.1045907 2.807604e-23 *
## 4 target:session 0.1126511 1.548507e-22 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF] p[HF]<.05
## 2 target 0.5275905 0.7830619 0.5294252 0.7839292
## 4 target:session 0.5298437 0.4642873 0.5318314 0.4648923retentionBayesANOVA()## Retention of learned performance, trained hand:
## Bayes factor analysis
## --------------
## [1] target + participant : 0.04065756 ±0.92%
## [2] session + participant : 0.1305003 ±1.08%
## [3] target + session + participant : 0.005343156 ±1.39%
## [4] target + session + target:session + participant : 0.0005354796 ±1.65%
##
## Against denominator:
## percentcomp ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.60 0.04 0.027
## session 0.60 0.12 0.087
## session:target 0.20 4.55e-04 0.002
##
## * Compared among: all models
## * Priors odds: uniform-equalWe find no effects of target and session, suggesting that reaching performance did not differ from the end of session 1 to the beginning of session 2, which is evidence of offline gains. We note however, that participants were not compensating for the very first trial, but were immediately able to compensate for the perturbation by the next trial. Thus, we are unable to disentangle whether we are observing retention or fast learning as we did in session 1 (but see movement analysis below).
Generalization across the workspace and hands
To quantify generalization, we compare reaching performance across quadrants. We conduct a 3x3x2 (target x block x quadrant) within-subjects ANOVA to compare the first set of reaches to quadrant 1 with reaches in quadrant 4. We repeat this test but instead compare quadrant 1 with quadrant 2, quadrant 1 and reaches to quadrant 1 after switching hands (Quadrant 1L).
#Quadrant 1 vs Quadrant 4
learningANOVA2Quads(quadrantA= '1', quadrantB = '4')##
## Quadrants 1 and 4:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 target 2 94 5.8916551 0.003885107 * 0.0146024272
## 3 block 2 94 0.3048346 0.737971303 0.0008071270
## 4 quadrant 1 47 0.8786223 0.353371233 0.0007741419
## 5 target:block 4 188 0.2784957 0.891631979 0.0015472166
## 6 target:quadrant 2 94 1.2733422 0.284677410 0.0019757918
## 7 block:quadrant 2 94 1.2105113 0.302647911 0.0027893757
## 8 target:block:quadrant 4 188 0.5598059 0.692116899 0.0023264191
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 2 target 0.100746692 1.186611e-23 *
## 3 block 0.927990833 1.792688e-01
## 5 target:block 0.004529887 1.770413e-47 *
## 6 target:quadrant 0.106500049 4.256431e-23 *
## 7 block:quadrant 0.881173420 5.450194e-02
## 8 target:block:quadrant 0.002467970 2.873020e-53 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 2 target 0.5265227 0.01755037 * 0.5282851 0.01745198
## 3 block 0.9328278 0.72283412 0.9698986 0.73133737
## 5 target:block 0.4789119 0.74812213 0.4987933 0.75701776
## 6 target:quadrant 0.5281225 0.26718582 0.5299933 0.26733147
## 7 block:quadrant 0.8937936 0.29982226 0.9267829 0.30079397
## 8 target:block:quadrant 0.4551332 0.55734524 0.4724800 0.56364957
## p[HF]<.05
## 2 *
## 3
## 5
## 6
## 7
## 8learningBayesANOVA2Quads(quadrantA= '1', quadrantB = '4')## Quadrants 1 and 4:
## Bayes factor analysis
## --------------
## [1] target + participant : 7.507861 ±0.92%
## [2] block + participant : 0.01888209 ±1.58%
## [3] target + block + participant : 0.1412734 ±1.74%
## [4] target + block + target:block + participant : 0.0009620405 ±2.46%
## [5] quadrant + participant : 0.104263 ±1.19%
## [6] target + quadrant + participant : 0.7974232 ±1.49%
## [7] block + quadrant + participant : 0.001941875 ±1.25%
## [8] target + block + quadrant + participant : 0.01441581 ±1.52%
## [9] target + block + target:block + quadrant + participant : 0.0001034858 ±4.06%
## [10] target + quadrant + target:quadrant + participant : 0.04722956 ±2.38%
## [11] target + block + quadrant + target:quadrant + participant : 0.0009723473 ±7.85%
## [12] target + block + target:block + quadrant + target:quadrant + participant : 6.288281e-06 ±8.04%
## [13] block + quadrant + block:quadrant + participant : 0.000161526 ±2.79%
## [14] target + block + quadrant + block:quadrant + participant : 0.001350278 ±6.05%
## [15] target + block + target:block + quadrant + block:quadrant + participant : 8.351922e-06 ±2.9%
## [16] target + block + quadrant + target:quadrant + block:quadrant + participant : 7.032091e-05 ±2.94%
## [17] target + block + target:block + quadrant + target:quadrant + block:quadrant + participant : 5.574736e-07 ±17.62%
## [18] target + block + target:block + quadrant + target:quadrant + block:quadrant + target:block:quadrant + participant : 1.266275e-08 ±4.71%
##
## Against denominator:
## percentcomp ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 0.88 2.70
## block 0.74 0.02 0.007
## block:target 0.32 1.12e-04 2.43e-04
## quadrant 0.74 0.10 0.040
## quadrant:target 0.32 5.01e-03 0.011
## block:quadrant 0.32 1.65e-04 3.58e-04
## block:quadrant:target 0.05 1.31e-09 2.37e-08
##
## * Compared among: all models
## * Priors odds: uniform-equal#Quadrant 1 vs Quadrant 2
learningANOVA2Quads(quadrantA= '1', quadrantB = '2')##
## Quadrants 1 and 2:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 target 2 94 1.84904930 0.1630654 0.0049078740
## 3 block 2 94 0.82551957 0.4411574 0.0018249315
## 4 quadrant 1 47 0.12966240 0.7203955 0.0001268186
## 5 target:block 4 188 0.09125076 0.9851202 0.0004377990
## 6 target:quadrant 2 94 0.03618134 0.9644788 0.0000685478
## 7 block:quadrant 2 94 0.07373624 0.9289703 0.0001821408
## 8 target:block:quadrant 4 188 0.02912671 0.9983517 0.0001309384
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 2 target 0.057477792 2.941045e-29 *
## 3 block 0.982121233 6.603852e-01
## 5 target:block 0.003400568 3.283442e-50 *
## 6 target:quadrant 0.104952607 3.039795e-23 *
## 7 block:quadrant 0.985523240 7.150526e-01
## 8 target:block:quadrant 0.007458604 9.745301e-43 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 2 target 0.5147946 0.1801961 0.5157696 0.1801824
## 3 block 0.9824353 0.4393510 1.0249086 0.4411574
## 5 target:block 0.5079766 0.9154345 0.5311072 0.9224177
## 6 target:quadrant 0.5276913 0.8620916 0.5295328 0.8628589
## 7 block:quadrant 0.9857298 0.9268326 1.0285706 0.9289703
## 8 target:block:quadrant 0.5206159 0.9746030 0.5452116 0.9780324
## p[HF]<.05
## 2
## 3
## 5
## 6
## 7
## 8learningBayesANOVA2Quads(quadrantA= '1', quadrantB = '2')## Quadrants 1 and 2:
## Bayes factor analysis
## --------------
## [1] target + participant : 0.1115488 ±0.55%
## [2] block + participant : 0.02999711 ±2.34%
## [3] target + block + participant : 0.003403034 ±1.6%
## [4] target + block + target:block + participant : 1.441883e-05 ±1.82%
## [5] quadrant + participant : 0.07864109 ±0.9%
## [6] target + quadrant + participant : 0.00889225 ±1.96%
## [7] block + quadrant + participant : 0.002342836 ±1.5%
## [8] target + block + quadrant + participant : 0.0002638133 ±1.92%
## [9] target + block + target:block + quadrant + participant : 1.405832e-06 ±17.11%
## [10] target + quadrant + target:quadrant + participant : 0.0002326421 ±1.7%
## [11] target + block + quadrant + target:quadrant + participant : 6.759523e-06 ±2.01%
## [12] target + block + target:block + quadrant + target:quadrant + participant : 3.086378e-08 ±4.65%
## [13] block + quadrant + block:quadrant + participant : 6.435804e-05 ±2.9%
## [14] target + block + quadrant + block:quadrant + participant : 7.135219e-06 ±2.81%
## [15] target + block + target:block + quadrant + block:quadrant + participant : 3.027357e-08 ±1.98%
## [16] target + block + quadrant + target:quadrant + block:quadrant + participant : 1.943736e-07 ±3.16%
## [17] target + block + target:block + quadrant + target:quadrant + block:quadrant + participant : 7.804978e-10 ±2.09%
## [18] target + block + target:block + quadrant + target:quadrant + block:quadrant + target:block:quadrant + participant : 9.326167e-12 ±2.26%
##
## Against denominator:
## percentcomp ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 0.10 0.040
## block 0.74 0.03 0.011
## block:target 0.32 1.29e-05 2.79e-05
## quadrant 0.74 0.07 0.028
## quadrant:target 0.32 1.94e-04 4.20e-04
## block:quadrant 0.32 5.81e-05 1.26e-04
## block:quadrant:target 0.05 7.55e-12 1.36e-10
##
## * Compared among: all models
## * Priors odds: uniform-equal#Quadrant 1 vs Switch hands, Quadrant 1
learningANOVA2Quads(quadrantA= '1', quadrantB = '1L')##
## Quadrants 1 and 1L:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 target 2 94 0.4256363 0.6546068 0.001463417
## 3 block 2 94 1.1517534 0.3205017 0.002782252
## 4 quadrant 1 47 1.7685407 0.1899809 0.001606810
## 5 target:block 4 188 0.4908462 0.7424620 0.002320116
## 6 target:quadrant 2 94 0.6213553 0.5394075 0.001009166
## 7 block:quadrant 2 94 0.7677213 0.4669568 0.001468688
## 8 target:block:quadrant 4 188 0.4289964 0.7875806 0.001696419
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 2 target 0.067796709 1.311590e-27 *
## 3 block 0.972897153 5.315443e-01
## 5 target:block 0.002971566 1.699690e-51 *
## 6 target:quadrant 0.094253831 2.563759e-24 *
## 7 block:quadrant 0.902193152 9.373226e-02
## 8 target:block:quadrant 0.002926948 1.219134e-51 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 2 target 0.5175439 0.5240269 0.5187023 0.5244626
## 3 block 0.9736123 0.3196110 1.0151071 0.3205017
## 5 target:block 0.4917545 0.6105808 0.5130509 0.6184553
## 6 target:quadrant 0.5247289 0.4417076 0.5263700 0.4421743
## 7 block:quadrant 0.9109071 0.4561049 0.9456674 0.4604638
## 8 target:block:quadrant 0.4507149 0.6317763 0.4676029 0.6390977
## p[HF]<.05
## 2
## 3
## 5
## 6
## 7
## 8learningBayesANOVA2Quads(quadrantA= '1', quadrantB = '1L')## Quadrants 1 and 1L:
## Bayes factor analysis
## --------------
## [1] target + participant : 0.02519319 ±1%
## [2] block + participant : 0.04486117 ±0.56%
## [3] target + block + participant : 0.001152058 ±1.24%
## [4] target + block + target:block + participant : 1.061787e-05 ±1.58%
## [5] quadrant + participant : 0.1526815 ±1%
## [6] target + quadrant + participant : 0.00393222 ±1.4%
## [7] block + quadrant + participant : 0.006883715 ±1.52%
## [8] target + block + quadrant + participant : 0.0001725947 ±1.44%
## [9] target + block + target:block + quadrant + participant : 1.74604e-06 ±6.24%
## [10] target + quadrant + target:quadrant + participant : 0.0001529211 ±2.29%
## [11] target + block + quadrant + target:quadrant + participant : 7.360302e-06 ±4.55%
## [12] target + block + target:block + quadrant + target:quadrant + participant : 6.281337e-08 ±2.53%
## [13] block + quadrant + block:quadrant + participant : 0.0003411365 ±2.46%
## [14] target + block + quadrant + block:quadrant + participant : 8.833139e-06 ±3.11%
## [15] target + block + target:block + quadrant + block:quadrant + participant : 8.361283e-08 ±4.1%
## [16] target + block + quadrant + target:quadrant + block:quadrant + participant : 3.460995e-07 ±4.04%
## [17] target + block + target:block + quadrant + target:quadrant + block:quadrant + participant : 3.213835e-09 ±6.24%
## [18] target + block + target:block + quadrant + target:quadrant + block:quadrant + target:block:quadrant + participant : 6.321119e-11 ±2.57%
##
## Against denominator:
## percentcomp ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 0.02 0.009
## block 0.74 0.04 0.016
## block:target 0.32 1.01e-05 2.19e-05
## quadrant 0.74 0.13 0.055
## quadrant:target 0.32 1.30e-04 2.82e-04
## block:quadrant 0.32 2.84e-04 6.15e-04
## block:quadrant:target 0.05 5.12e-11 9.21e-10
##
## * Compared among: all models
## * Priors odds: uniform-equalWe find no effects of quadrant, suggesting that overall reaching performance did not differ between each comparison of quadrants. This is evidence that participants are able to transfer learning to other target locations and to their untrained hand.
We did find a target effect when comparing quadrant 1 and quadrant 4, which is likely driven by the target effect we observed for the analysis within quadrant 4 above.
Q1and4ComparisonsEffSize()## contrast estimate SE df t.ratio p.value
## Far vs. Mid -10.7 5.48 47 -1.952 0.1708
## Far vs. Near 61.7 28.46 47 2.166 0.1061
## Mid vs. Near 72.4 26.71 47 2.709 0.0281
##
## P value adjustment: bonferroni method for 3 tests
## contrast etasquared
## 1 Far vs. Mid 0.07497162
## 2 Far vs. Near 0.09079807
## 3 Mid vs. Near 0.13507653Q1and4ComparisonsBayesfollowup()## Bayesian t-test far vs mid target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 1.004491 ±0.01%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test far vs near target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 1.604116 ±0.01%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test mid vs near target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 3.133569 ±0.01%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZSFollow-up tests confirm that this is the case. The effect is driven by the difference in compensation between middle and near targets, regardless of block or session.
Reach aftereffects for the untrained/ nondominant hand
First, we test for target or block effects within washout trials using the nondominant or untrained hand.
washoutLearningANOVA()## Quadrant 1W:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 block 2 94 15.1220397 2.023257e-06 * 0.042833644
## 3 target 2 94 3.5808510 3.171401e-02 * 0.017107267
## 4 block:target 4 188 0.8966133 4.670917e-01 0.008680658
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 2 block 0.9057849 0.10270157
## 3 target 0.8426683 0.01950308 *
## 4 block:target 0.7970306 0.32682005
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 2 block 0.9138971 4.800909e-06 * 0.9489699 3.375679e-06
## 3 target 0.8640565 3.856491e-02 * 0.8940364 3.693677e-02
## 4 block:target 0.8950415 4.585455e-01 0.9779399 4.653805e-01
## p[HF]<.05
## 2 *
## 3 *
## 4washoutLearningBayesANOVA()## Quadrant 1W:
## Bayes factor analysis
## --------------
## [1] target + participant : 0.939413 ±0.56%
## [2] block + participant : 342.5456 ±0.78%
## [3] target + block + participant : 407.2919 ±3.11%
## [4] target + block + target:block + participant : 23.84221 ±8.12%
##
## Against denominator:
## angdev ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.60 0.56 0.838
## block 0.60 1.00 265.95
## block:target 0.20 0.03 0.127
##
## * Compared among: all models
## * Priors odds: uniform-equalWe find main effects of block and target, but no interaction. In the Bayesian test, we only find the effect of block.
washoutComparisonsEffSize()## contrast estimate SE df t.ratio p.value
## block 1 vs. block 2 -22.43 4.82 47 -4.656 0.0001
## block 1 vs. block 3 -25.00 5.69 47 -4.394 0.0002
## block 2 vs. block 3 -2.57 4.41 47 -0.584 1.0000
##
## P value adjustment: bonferroni method for 3 tests
## contrast etasquared
## 1 block 1 vs. block 2 0.315654642
## 2 block 1 vs. block 3 0.291160194
## 3 block 2 vs. block 3 0.007194419washoutComparisonsBayesfollowup()## Bayesian t-test block 1 vs block 2:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 36.5822 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test block 1 vs last block:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 90.75674 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test block 2 vs last block:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.2393834 ±0.02%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZSFollow-up tests show that the effect of block is driven by the difference of the first block of washout trials with the other blocks. This confirms what we see in the plot, where initially participants are compensating in the first washout trial. However, this is likely due to task switching rather than aftereffects, as participants were not instructed that the perturbation has been turned off.
washoutTargetEffectComparisonsEffSize()## contrast estimate SE df t.ratio p.value
## Far vs. Mid 4.42 7.50 47 0.589 1.0000
## Far vs. Near -12.14 6.21 47 -1.956 0.1693
## Mid vs. Near -16.56 5.33 47 -3.108 0.0096
##
## P value adjustment: bonferroni method for 3 tests
## contrast etasquared
## 1 Far vs. Mid 0.007324856
## 2 Far vs. Near 0.075266800
## 3 Mid vs. Near 0.170452381washoutTargetEffectComparisonsBayesfollowup()## Bayesian t-test far vs mid target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.2530544 ±0.02%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test far vs near target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.7944837 ±0.01%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test mid vs near target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 3.549782 ±0.01%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZSFollow-up tests on the target effect show that the middle target differs from the near target.
To test for reach aftereffects, we can compare reaching performance between perturbed reaches with the nondominant hand (Quadrant 1L) and washout trials (Quadrant 1W). We conduct a 3x3x2 (target x block x quadrant) within-subjects ANOVA.
learningANOVA2Quads(quadrantA='1L', quadrantB='1W')##
## Quadrants 1L and 1W:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 target 2 94 0.2121945 0.809193762 0.0009492916
## 3 block 2 94 0.5591720 0.573571982 0.0008790317
## 4 quadrant 1 47 10.3977196 0.002297113 * 0.0112591076
## 5 target:block 4 188 0.3227002 0.862526463 0.0010402147
## 6 target:quadrant 2 94 0.6193692 0.540465967 0.0010870928
## 7 block:quadrant 2 94 3.6627790 0.029391107 * 0.0073364691
## 8 target:block:quadrant 4 188 1.5835445 0.180365277 0.0069801660
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 2 target 0.076882147 2.365846e-26 *
## 3 block 0.930398794 1.902787e-01
## 5 target:block 0.007872065 3.168663e-42 *
## 6 target:quadrant 0.079828186 5.618158e-26 *
## 7 block:quadrant 0.936877156 2.232035e-01
## 8 target:block:quadrant 0.002004223 2.954314e-55 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 2 target 0.5199889 0.65676290 0.5213111 0.65738333
## 3 block 0.9349279 0.56219811 0.9722224 0.56880561
## 5 target:block 0.4795409 0.71597892 0.4994908 0.72477079
## 6 target:quadrant 0.5207867 0.44132898 0.5221624 0.44172426
## 7 block:quadrant 0.9406251 0.03212481 * 0.9785290 0.03035145
## 8 target:block:quadrant 0.4835486 0.21146933 0.5039371 0.21047612
## p[HF]<.05
## 2
## 3
## 5
## 6
## 7 *
## 8learningBayesANOVA2Quads(quadrantA='1L', quadrantB='1W')## Quadrants 1L and 1W:
## Bayes factor analysis
## --------------
## [1] target + participant : 0.02006716 ±0.79%
## [2] block + participant : 0.01953694 ±0.98%
## [3] target + block + participant : 0.0004045415 ±2.52%
## [4] target + block + target:block + participant : 2.286345e-06 ±4.2%
## [5] quadrant + participant : 13.25757 ±1.64%
## [6] target + quadrant + participant : 0.2638982 ±1.57%
## [7] block + quadrant + participant : 0.255889 ±3.09%
## [8] target + block + quadrant + participant : 0.005076807 ±1.83%
## [9] target + block + target:block + quadrant + participant : 2.973018e-05 ±4.56%
## [10] target + quadrant + target:quadrant + participant : 0.01123886 ±4.97%
## [11] target + block + quadrant + target:quadrant + participant : 0.0002195478 ±5.06%
## [12] target + block + target:block + quadrant + target:quadrant + participant : 1.164891e-06 ±2.44%
## [13] block + quadrant + block:quadrant + participant : 0.1641339 ±3.07%
## [14] target + block + quadrant + block:quadrant + participant : 0.003286089 ±2.66%
## [15] target + block + target:block + quadrant + block:quadrant + participant : 1.901916e-05 ±5.16%
## [16] target + block + quadrant + target:quadrant + block:quadrant + participant : 0.000142566 ±3.59%
## [17] target + block + target:block + quadrant + target:quadrant + block:quadrant + participant : 7.704212e-07 ±6.83%
## [18] target + block + target:block + quadrant + target:quadrant + block:quadrant + target:block:quadrant + participant : 1.110463e-07 ±3.03%
##
## Against denominator:
## percentcomp ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 0.02 0.007
## block 0.74 0.03 0.011
## block:target 0.32 3.54e-06 7.67e-06
## quadrant 0.74 0.93 4.79
## quadrant:target 0.32 7.73e-04 0.002
## block:quadrant 0.32 0.01 0.024
## block:quadrant:target 0.05 7.40e-09 1.33e-07
##
## * Compared among: all models
## * Priors odds: uniform-equalWe find a main effect of quadrant and a block by quadrant interaction in the frequentist test, but only find the main effect of quadrant in the Bayesian test. The main effect of quadrant is seen in the plot, where washout trials are near zero in compensation.
Q1Land1WComparisonsEffSize()## contrast estimate SE df t.ratio p.value
## Untrained_B3 vs. Washout_B1 -60.9 32.5 47 -1.873 0.2019
## Untrained_B3 vs. Washout_B2 -101.9 29.4 47 -3.461 0.0035
## Untrained_B3 vs. Washout_B3 -129.2 28.7 47 -4.507 0.0001
##
## P value adjustment: bonferroni method for 3 tests
## contrast etasquared
## 1 Untrained_B3 vs. Washout_B1 0.06944924
## 2 Untrained_B3 vs. Washout_B2 0.20309709
## 3 Untrained_B3 vs. Washout_B3 0.30177830Q1Land1WComparisonsBayesfollowup()## Bayesian t-test Untrained last block vs Washout block 1:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.7893392 ±0.01%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test Untrained last block vs Washout block 2:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 8.568513 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test Untrained last block vs Washout last block:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 242.7726 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZSFollow-up tests on the block by quadrant interaction show that the last block of mirror reversed training differs from the second and last blocks of washout trials. The lack of a difference between the first washout block from the training block is likely due to task switching rather than aftereffects, as participants were not instructed that the perturbation has been turned off.
Finally, we compare the washout trials with the aligned baseline trials using the nondominant hand from the first session. We conduct a 3x3x2 (target x block x session) within-subjects ANOVA.
RAEUntrainedHandANOVA()## Comparing angular reach deviations during washout trials with aligned trials across targets and blocks, trained hand:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 block 2 94 15.7677651 1.244446e-06 * 0.022927060
## 3 target 2 94 1.5553541 2.164983e-01 0.002820846
## 4 session 1 47 0.4072721 5.264547e-01 0.001023962
## 5 block:target 4 188 0.6579821 6.219550e-01 0.003012623
## 6 block:session 2 94 3.3679176 3.866887e-02 * 0.005469397
## 7 target:session 2 94 2.2674716 1.092110e-01 0.007782668
## 8 block:target:session 4 188 0.9187853 4.541233e-01 0.004281288
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 2 block 0.7877256 0.004136416 *
## 3 target 0.9822852 0.662925419
## 5 block:target 0.5634645 0.002017964 *
## 6 block:session 0.9972799 0.939274660
## 7 target:session 0.9304575 0.190555106
## 8 block:target:session 0.8508408 0.602462907
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 2 block 0.8248958 7.831655e-06 * 0.8510434 5.947292e-06
## 3 target 0.9825935 2.168773e-01 1.0250845 2.164983e-01
## 5 block:target 0.7478645 5.788274e-01 0.8043323 5.895535e-01
## 6 block:session 0.9972873 3.880391e-02 * 1.0414253 3.866887e-02
## 7 target:session 0.9349792 1.130313e-01 0.9722792 1.108290e-01
## 8 block:target:session 0.9201433 4.482822e-01 1.0080207 4.541233e-01
## p[HF]<.05
## 2 *
## 3
## 5
## 6 *
## 7
## 8RAEUntrainedHandBayesANOVA()## Comparing angular reach deviations during washout trials with aligned trials across targets and blocks, trained hand:
## Bayes factor analysis
## --------------
## [1] target + participant : 0.04203115 ±0.71%
## [2] block + participant : 214.7836 ±1.02%
## [3] target + block + participant : 9.453578 ±3.55%
## [4] target + block + target:block + participant : 0.1050482 ±1.53%
## [5] session + participant : 0.114371 ±1.02%
## [6] target + session + participant : 0.004934808 ±2.85%
## [7] block + session + participant : 24.60886 ±1.68%
## [8] target + block + session + participant : 1.091554 ±3.22%
## [9] target + block + target:block + session + participant : 0.01526409 ±20.32%
## [10] target + session + target:session + participant : 0.002758292 ±1.5%
## [11] target + block + session + target:session + participant : 0.6726054 ±3.97%
## [12] target + block + target:block + session + target:session + participant : 0.007442536 ±2.46%
## [13] block + session + block:session + participant : 5.790545 ±1.86%
## [14] target + block + session + block:session + participant : 0.2569278 ±2.95%
## [15] target + block + target:block + session + block:session + participant : 0.002857228 ±2.67%
## [16] target + block + session + target:session + block:session + participant : 0.1576944 ±2.12%
## [17] target + block + target:block + session + target:session + block:session + participant : 0.001842321 ±2.19%
## [18] target + block + target:block + session + target:session + block:session + target:block:session + participant : 9.384698e-05 ±3.42%
##
## Against denominator:
## angdev ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 0.05 0.017
## block 0.74 1.00 78.83
## block:target 0.32 5.14e-04 0.001
## session 0.74 0.13 0.052
## session:target 0.32 3.26e-03 0.007
## block:session 0.32 0.02 0.053
## block:session:target 0.05 3.64e-07 6.54e-06
##
## * Compared among: all models
## * Priors odds: uniform-equalWe find a main effect of block and a block by session interaction in the frequentist test, but only a main effect of block in the Bayesian test. We look into the interaction further.
untrainedHandSessionComparisonsEffSize()## contrast estimate SE df t.ratio p.value
## Baseline_B1 vs. Washout_B1 13.418 7.33 47 1.831 0.2940
## Baseline_B2 vs. Washout_B2 -0.649 5.42 47 -0.120 1.0000
## Baseline_B3 vs. Washout_B3 -3.277 6.21 47 -0.528 1.0000
## Baseline_B3 vs. Washout_B1 21.722 8.47 47 2.564 0.0544
##
## P value adjustment: bonferroni method for 4 tests
## contrast etasquared
## 1 Baseline_B1 vs. Washout_B1 0.0665584359
## 2 Baseline_B2 vs. Washout_B2 0.0003052035
## 3 Baseline_B3 vs. Washout_B3 0.0058888713
## 4 Baseline_B3 vs. Washout_B1 0.1227421759untrainedHandSessionComparisonsBayesfollowup()## Bayesian t-test Untrained block 1 vs Washout block 1:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 1.377666 ±0.01%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test Untrained block 2 vs Washout block 2:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.21636 ±0.02%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test Untrained last block vs Washout last block:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.2479524 ±0.02%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test Untrained last block vs Washout block 1:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 14.91385 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZSWe find no significant effects, but Bayesian follow-up tests show that the effect is driven by a difference between the last block of aligned reaches and the first block of washout trials. Again, this is likely due to higher compensation percentages during the first washout trial. Overall, the data suggest that we do not observe reach aftereffects, given that the compensation percentages ion the first block immediately go back down to zero.
Movement analysis
We then repeat the same set of tests but instead use completion time and path length as the dependent variables.
Completion time
plotCtrlGenMT()
Learned performance
We first tested for target or block effects for completion time within each quadrant. Thus, we conducted 3x3 (target x block) within-subjects ANOVA for quadrants 1, 4, 2, top-up trials in quadrant 1 (Quadrant 1A in tests below), quadrant 1 after switching hands (Quadrant 1L in tests below), and washout (Quadrant 1W).
movementtimeANOVA()## Quadrant 1:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 block 2 94 29.988308 8.445684e-11 * 0.07926953
## 3 target 2 94 22.691070 9.104875e-09 * 0.07753893
## 4 block:target 4 188 6.768633 4.128631e-05 * 0.02684214
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 2 block 0.8705848 0.0412718912 *
## 3 target 0.9655023 0.4459907989
## 4 block:target 0.4856140 0.0001459336 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 2 block 0.8854139 8.059114e-10 * 0.9175465 4.279397e-10
## 3 target 0.9666527 1.509580e-08 * 1.0073809 9.104875e-09
## 4 block:target 0.7468240 2.751544e-04 * 0.8031216 1.801157e-04
## p[HF]<.05
## 2 *
## 3 *
## 4 *
##
## Quadrant 4:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 block 2 94 16.489051 7.273679e-07 * 0.039070346
## 3 target 2 94 26.787957 6.212716e-10 * 0.116236200
## 4 block:target 4 188 1.207168 3.092103e-01 0.004833261
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 2 block 0.9357585 0.2171533270
## 3 target 0.9327692 0.2017466183
## 4 block:target 0.4761912 0.0001021447 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 2 block 0.9396363 1.412572e-06 * 0.9774342 9.321046e-07
## 3 target 0.9370044 1.900460e-09 * 0.9745207 9.763744e-10
## 4 block:target 0.7388727 3.093910e-01 0.7938762 3.097165e-01
## p[HF]<.05
## 2 *
## 3 *
## 4
##
## Quadrant 2:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 block 2 94 6.469677 0.0023310086 * 0.02304146
## 3 target 2 94 8.721093 0.0003354878 * 0.04022956
## 4 block:target 4 188 1.751156 0.1405219557 0.01278021
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 2 block 0.394679939 5.171734e-10 *
## 3 target 0.483647559 5.548390e-08 *
## 4 block:target 0.004496498 1.447918e-47 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF] p[HF]<.05
## 2 block 0.6229287 0.009148997 * 0.6316495 0.008862699 *
## 3 target 0.6594773 0.002072488 * 0.6710641 0.001947239 *
## 4 block:target 0.2972558 0.191432917 0.3005454 0.191332246
##
## Quadrant 1A:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 block 2 94 3.2454705 4.335550e-02 * 0.011124427
## 3 target 2 94 21.2971347 2.353329e-08 * 0.083466404
## 4 block:target 4 188 0.7981263 5.277666e-01 0.003183879
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 2 block 0.8156959 0.009228921 *
## 3 target 0.9890115 0.775587440
## 4 block:target 0.7693944 0.218961295
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 2 block 0.8443778 5.223148e-02 0.8724133 5.051059e-02
## 3 target 0.9891309 2.747553e-08 * 1.0323521 2.353329e-08
## 4 block:target 0.8823321 5.143004e-01 0.9627627 5.236786e-01
## p[HF]<.05
## 2
## 3 *
## 4
##
## Quadrant 1L:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 block 2 94 8.603618 3.704724e-04 * 0.03399100
## 3 target 2 94 15.036605 2.158452e-06 * 0.05695070
## 4 block:target 4 188 2.755522 2.930339e-02 * 0.01792748
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 2 block 0.8376428 1.699630e-02 *
## 3 target 0.7244187 6.022292e-04 *
## 4 block:target 0.1782312 3.682601e-13 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 2 block 0.8603208 7.700717e-04 * 0.8899286 6.592323e-04
## 3 target 0.7839563 1.869548e-05 * 0.8062562 1.495161e-05
## 4 block:target 0.5155141 6.691299e-02 0.5395146 6.421320e-02
## p[HF]<.05
## 2 *
## 3 *
## 4
##
## Quadrant 1W:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 block 2 94 84.296172 1.073377e-21 * 0.14988439
## 3 target 2 94 6.217149 2.911884e-03 * 0.02257217
## 4 block:target 4 188 5.042584 6.984433e-04 * 0.03439951
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 2 block 0.8843819 5.925380e-02
## 3 target 0.7321301 7.682983e-04 *
## 4 block:target 0.1103566 1.652471e-17 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 2 block 0.8963641 1.057847e-19 * 0.9296176 2.423986e-20
## 3 target 0.7887245 6.001518e-03 * 0.8114642 5.550609e-03
## 4 block:target 0.5059106 8.068637e-03 * 0.5288047 7.190475e-03
## p[HF]<.05
## 2 *
## 3 *
## 4 *movementtimeBayesANOVA()## Quadrant 1:
## Bayes factor analysis
## --------------
## [1] target + participant : 385877701 ±3.65%
## [2] block + participant : 677993264 ±0.55%
## [3] target + block + participant : 8.208533e+18 ±1.48%
## [4] target + block + target:block + participant : 3.764873e+20 ±1.5%
##
## Against denominator:
## movementtime ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.60 1.00 3.78e+11
## block 0.60 1.00 6.65e+11
## block:target 0.20 0.98 183.46
##
## * Compared among: all models
## * Priors odds: uniform-equalQuadrant 4:
## Bayes factor analysis
## --------------
## [1] target + participant : 5.091319e+14 ±4.38%
## [2] block + participant : 1059.443 ±0.96%
## [3] target + block + participant : 5.959366e+18 ±1.83%
## [4] target + block + target:block + participant : 2.494715e+17 ±1.3%
##
## Against denominator:
## movementtime ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.60 1.00 3.90e+15
## block 0.60 1.00 8.13e+03
## block:target 0.20 0.04 0.167
##
## * Compared among: all models
## * Priors odds: uniform-equalQuadrant 2:
## Bayes factor analysis
## --------------
## [1] target + participant : 355.43 ±0.64%
## [2] block + participant : 5.104799 ±0.87%
## [3] target + block + participant : 2427.61 ±1.61%
## [4] target + block + target:block + participant : 362.3068 ±1.42%
##
## Against denominator:
## movementtime ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.60 1.00 343.48
## block 0.60 0.89 5.23
## block:target 0.20 0.11 0.520
##
## * Compared among: all models
## * Priors odds: uniform-equalQuadrant 1A:
## Bayes factor analysis
## --------------
## [1] target + participant : 17901277361 ±0.78%
## [2] block + participant : 0.5718118 ±1.72%
## [3] target + block + participant : 16737851641 ±1.79%
## [4] target + block + target:block + participant : 469888630 ±7.53%
##
## Against denominator:
## movementtime ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.60 1.00 1.49e+10
## block 0.60 0.49 0.641
## block:target 0.20 0.01 0.054
##
## * Compared among: all models
## * Priors odds: uniform-equalQuadrant 1L:
## Bayes factor analysis
## --------------
## [1] target + participant : 38277.62 ±0.94%
## [2] block + participant : 85.5004 ±1.09%
## [3] target + block + participant : 6074525 ±1.11%
## [4] target + block + target:block + participant : 3654912 ±1.77%
##
## Against denominator:
## movementtime ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.60 1.00 7.53e+04
## block 0.60 1.00 169.45
## block:target 0.20 0.37 2.39
##
## * Compared among: all models
## * Priors odds: uniform-equalQuadrant 1W:
## Bayes factor analysis
## --------------
## [1] target + participant : 3.843569 ±0.69%
## [2] block + participant : 1.985082e+17 ±0.59%
## [3] target + block + participant : 2.889138e+18 ±0.85%
## [4] target + block + target:block + participant : 2.486647e+20 ±1.3%
##
## Against denominator:
## movementtime ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.60 1.00 844.81
## block 0.60 1.00 3.47e+19
## block:target 0.20 0.99 322.14
##
## * Compared among: all models
## * Priors odds: uniform-equalIn quadrant 1, we find a significant target x block interaction. We know from the plot that completion time decreases across blocks. Thus, it is more interesting to test for target differences across the blocks of trials.
quadrant1MTComparisonsEffSize()## contrast estimate SE df t.ratio p.value
## 1st block: Far vs. Mid 1.4475 0.311 47 4.652 0.0002
## 1st block: Far vs. Near 0.4043 0.178 47 2.271 0.2499
## 1st block: Mid vs. Near -1.0432 0.294 47 -3.552 0.0079
## 2nd block: Far vs. Mid 0.9987 0.194 47 5.159 <.0001
## 2nd block: Far vs. Near 1.0510 0.252 47 4.165 0.0012
## 2nd block: Mid vs. Near 0.0522 0.291 47 0.179 1.0000
## last block: Far vs. Mid 0.5965 0.105 47 5.689 <.0001
## last block: Far vs. Near 0.9546 0.186 47 5.140 <.0001
## last block: Mid vs. Near 0.3581 0.176 47 2.034 0.4284
##
## P value adjustment: bonferroni method for 9 tests
## contrast etasquared
## 1 1st block: Far vs. Mid 0.3152674083
## 2 1st block: Far vs. Near 0.0988854403
## 3 1st block: Mid vs. Near 0.2116270196
## 4 2nd block: Far vs. Mid 0.3615263646
## 5 2nd block: Far vs. Near 0.2695574551
## 6 2nd block: Mid vs. Near 0.0006849891
## 7 last block: Far vs. Mid 0.4077606145
## 8 last block: Far vs. Near 0.3598773765
## 9 last block: Mid vs. Near 0.0809123753quadrant1MTComparisonsBayesfollowup()## Bayesian t-test block 1 far vs mid target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 205.2714 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test block 1 far vs near target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.5159219 ±0.02%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test block 1 mid vs near target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 4.409246 ±0.01%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test block 2 far vs mid target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 20.65155 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test block 2 far vs near target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 8.936921 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test block 2 mid vs near target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.2162143 ±0.02%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test last block far vs mid target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 210.7423 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test last block far vs near target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 956.9907 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test last block mid vs near target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.6495352 ±0.02%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZSFollow-up tests show that the completion time for the far target is faster compared to the middle target in all blocks, and faster compared to the near target in the second and last blocks. Completion time was also faster for the near target compared to the middle target in the first block. This suggests that movement initiation and execution was fastest for the far target and slowest for the middle target.
For quadrants 4, 2 and top-up trials to quadrant 1 (Quadrant 1A), we observe main effects of target. We also observe main effects of block for quadrant 4 and 2, but this is seen with the decrease of completion time from the plot.
#quadrant 4
quadrant4MTComparisonsEffSizeTargetEffect()## contrast estimate SE df t.ratio p.value
## Far vs. Mid 1.021 0.151 47 6.752 <.0001
## Far vs. Near 0.649 0.122 47 5.337 <.0001
## Mid vs. Near -0.372 0.149 47 -2.500 0.0479
##
## P value adjustment: bonferroni method for 3 tests
## contrast etasquared
## 1 Far vs. Mid 0.4924049
## 2 Far vs. Near 0.3773268
## 3 Mid vs. Near 0.1173990quadrant4MTComparisonsTargetEffectBayesfollowup()## Bayesian t-test far vs mid target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 7582.645 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test far vs near target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 117.5709 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test mid vs near target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.7023399 ±0.02%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS#quadrant 2
quadrant2MTComparisonsEffSizeTargetEffect()## contrast estimate SE df t.ratio p.value
## Far vs. Mid 0.857 0.246 47 3.487 0.0032
## Far vs. Near 0.577 0.111 47 5.195 <.0001
## Mid vs. Near -0.280 0.242 47 -1.156 0.7608
##
## P value adjustment: bonferroni method for 3 tests
## contrast etasquared
## 1 Far vs. Mid 0.20556384
## 2 Far vs. Near 0.36473769
## 3 Mid vs. Near 0.02763747quadrant2MTComparisonsTargetEffectBayesfollowup()## Bayesian t-test far vs mid target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 17.8396 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test far vs near target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 27.84951 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test mid vs near target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.3211038 ±0.02%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS#quadrant 1 (top-up trials)
quadrant1AMTComparisonsEffSizeTargetEffect()## contrast estimate SE df t.ratio p.value
## Far vs. Mid 0.5973 0.1038 47 5.753 <.0001
## Far vs. Near 0.5378 0.1030 47 5.220 <.0001
## Mid vs. Near -0.0595 0.0954 47 -0.623 1.0000
##
## P value adjustment: bonferroni method for 3 tests
## contrast etasquared
## 1 Far vs. Mid 0.413240815
## 2 Far vs. Near 0.366961053
## 3 Mid vs. Near 0.008200663quadrant1AMTComparisonsTargetEffectBayesfollowup()## Bayesian t-test far vs mid target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 1173.483 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test far vs near target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 134.756 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test mid vs near target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.2263229 ±0.02%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZSIn all three quadrants, the target effect is accounted for by faster completion times for the far target, compared to the middle and near targets.
For completion times for reaches with the nondominant hand (Quadrant 1L), we find main effects of block and target. We follow up on the target effect.
quadrant1LMTComparisonsEffSizeTargetEffect()## contrast estimate SE df t.ratio p.value
## Far vs. Mid 0.930 0.180 47 5.166 <.0001
## Far vs. Near 0.712 0.129 47 5.507 <.0001
## Mid vs. Near -0.218 0.213 47 -1.026 0.9307
##
## P value adjustment: bonferroni method for 3 tests
## contrast etasquared
## 1 Far vs. Mid 0.36215145
## 2 Far vs. Near 0.39218503
## 3 Mid vs. Near 0.02189951quadrant1LMTComparisonsTargetEffectBayesfollowup()## Bayesian t-test far vs mid target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 124.5042 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test far vs near target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 46.58137 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test mid vs near target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.2926252 ±0.02%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZSAs in the other quadrants, we find that the far target had faster completion times that the middle or near targets.
Finally, for washout trials, we find a significant target x block interaction.
quadrant1WMTComparisonsEffSize()## contrast estimate SE df t.ratio p.value
## 1st block: Far vs. Mid 0.6277 0.1778 47 3.530 0.0085
## 1st block: Far vs. Near 0.2990 0.1417 47 2.110 0.3622
## 1st block: Mid vs. Near -0.3287 0.2235 47 -1.471 1.0000
## 2nd block: Far vs. Mid 0.0251 0.0543 47 0.462 1.0000
## 2nd block: Far vs. Near 0.0590 0.0494 47 1.194 1.0000
## 2nd block: Mid vs. Near 0.0339 0.0576 47 0.588 1.0000
## last block: Far vs. Mid 0.0266 0.0482 47 0.551 1.0000
## last block: Far vs. Near 0.1762 0.0573 47 3.072 0.0317
## last block: Mid vs. Near 0.1496 0.0591 47 2.533 0.1324
##
## P value adjustment: bonferroni method for 9 tests
## contrast etasquared
## 1 1st block: Far vs. Mid 0.209556261
## 2 1st block: Far vs. Near 0.086502033
## 3 1st block: Mid vs. Near 0.043993946
## 4 2nd block: Far vs. Mid 0.004521761
## 5 2nd block: Far vs. Near 0.029424307
## 6 2nd block: Mid vs. Near 0.007301822
## 7 last block: Far vs. Mid 0.006419407
## 8 last block: Far vs. Near 0.167253323
## 9 last block: Mid vs. Near 0.120109147quadrant1WMTComparisonsBayesfollowup()## Bayesian t-test block 1 far vs mid target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 20.89689 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test block 1 far vs near target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 1.026296 ±0.01%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test block 1 mid vs near target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.6117245 ±0.02%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test block 2 far vs mid target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.2210838 ±0.02%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test block 2 far vs near target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.252359 ±0.02%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test block 2 mid vs near target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.2241006 ±0.02%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test last block far vs mid target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.2265576 ±0.02%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test last block far vs near target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 1.533126 ±0.01%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test last block mid vs near target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.9868353 ±0.01%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZSFollow-up tests show faster completion times for the far target than the middle target in the first block, and faster completion times for the far target than the near target in the last block. Overall, these findings show that movement initiation and execution is faster for far targets.
Retention
To quantify retention, we compare the completion times between the last block of mirror reversed reaches in session 1, with the first block of mirror reversed reaches in session 2.
retentionMTANOVA()## Comparing completion times between session 1 and session 2 during learning, trained hand:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 target 2 94 25.06861 1.881618e-09 * 0.10626061
## 3 session 1 47 22.88924 1.737681e-05 * 0.06014891
## 4 target:session 2 94 7.06511 1.385148e-03 * 0.02330774
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 2 target 0.9496843 3.050161e-01
## 4 target:session 0.6016050 8.397762e-06 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 2 target 0.9520947 4.183383e-09 * 0.9912350 2.17770e-09
## 4 target:session 0.7151055 4.425399e-03 * 0.7312974 4.14135e-03
## p[HF]<.05
## 2 *
## 4 *retentionMTBayesANOVA()## Comparing completion times between session 1 and session 2 during learning, trained hand:
## Bayes factor analysis
## --------------
## [1] target + participant : 24902352 ±5.35%
## [2] session + participant : 5952.922 ±0.88%
## [3] target + session + participant : 1.182066e+12 ±3.82%
## [4] target + session + target:session + participant : 8.466785e+12 ±5.56%
##
## Against denominator:
## movementtime ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.60 1.00 1.08e+09
## session 0.60 1.00 2.58e+05
## session:target 0.20 0.88 28.65
##
## * Compared among: all models
## * Priors odds: uniform-equalWe find a significant target x session interaction.
part1and2MTComparisonsEffSize()## contrast estimate SE df t.ratio p.value
## Far: Part 1 vs Part 2 0.797 0.148 47 5.373 <.0001
## Mid: Part 1 vs Part 2 1.252 0.321 47 3.905 0.0009
## Near: Part 1 vs Part 2 0.157 0.178 47 0.882 1.0000
##
## P value adjustment: bonferroni method for 3 tests
## contrast etasquared
## 1 Far: Part 1 vs Part 2 0.38048775
## 2 Mid: Part 1 vs Part 2 0.24494853
## 3 Near: Part 1 vs Part 2 0.01628236part1and2MTComparisonsBayesfollowup()## Bayesian t-test part 1 far vs block 1 far:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 459.4583 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test part 1 mid vs block 1 mid:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 28.96823 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test part 1 near vs block 1 near:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.2398086 ±0.02%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZSFollow-up tests show that the far and middle targets had slightly slower completion times for the first block in session 2, compared to the last block in session 1. However, in comparing completion time plots, we see that the starting completion times in session 2 are faster than how participants started in session 1, suggesting that there was retention of learning.
Generalization across the workspace and hands
To quantify generalization, we compare completion time across quadrants. We conduct a 3x3x2 (target x block x quadrant) within-subjects ANOVA to compare the first set of reaches to quadrant 1 with reaches in quadrant 4. We repeat this test but instead compare quadrant 1 with quadrant 2, quadrant 1 and reaches to quadrant 1 after switching hands (Quadrant 1L).
#Quadrant 1 vs Quadrant 4
MTANOVA2Quads(quadrantA= '1', quadrantB = '4')## Quadrants 1 and 4:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 target 2 94 43.0095937 5.457901e-14 * 0.0917392794
## 3 block 2 94 48.1965805 3.920992e-15 * 0.0586027483
## 4 quadrant 1 47 11.7249548 1.288442e-03 * 0.0186295788
## 5 target:block 4 188 5.5070298 3.254943e-04 * 0.0097007844
## 6 target:quadrant 2 94 0.4238214 6.557853e-01 0.0007647514
## 7 block:quadrant 2 94 4.8227408 1.014242e-02 * 0.0068404355
## 8 target:block:quadrant 4 188 4.0869681 3.361144e-03 * 0.0092199631
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 2 target 0.9910914 0.813983454
## 3 block 0.9955659 0.902838816
## 5 target:block 0.5971613 0.005361389 *
## 6 target:quadrant 0.8090879 0.007654226 *
## 7 block:quadrant 0.9020354 0.093356133
## 8 target:block:quadrant 0.5803797 0.003332535 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 2 target 0.9911701 6.916235e-14 * 1.0346198 5.457901e-14
## 3 block 0.9955855 4.464306e-15 * 1.0395317 3.920992e-15
## 5 target:block 0.8158601 9.113391e-04 * 0.8839581 6.220516e-04
## 6 target:quadrant 0.8396925 6.208286e-01 0.8672707 6.272921e-01
## 7 block:quadrant 0.9107762 1.251744e-02 * 0.9455229 1.153186e-02
## 8 target:block:quadrant 0.7781078 7.338121e-03 * 0.8396267 5.903106e-03
## p[HF]<.05
## 2 *
## 3 *
## 5 *
## 6
## 7 *
## 8 *MTBayesANOVA2Quads(quadrantA= '1', quadrantB = '4')## Quadrants 1 and 4:
## Bayes factor analysis
## --------------
## [1] target + participant : 3.118989e+21 ±0.75%
## [2] block + participant : 1.255924e+12 ±0.77%
## [3] target + block + participant : 4.758211e+35 ±1.46%
## [4] target + block + target:block + participant : 4.459315e+35 ±6.16%
## [5] quadrant + participant : 1202.999 ±1.96%
## [6] target + quadrant + participant : 1.476318e+25 ±1.33%
## [7] block + quadrant + participant : 3.274925e+15 ±1.6%
## [8] target + block + quadrant + participant : 6.523962e+39 ±1.9%
## [9] target + block + target:block + quadrant + participant : 6.74472e+39 ±1.37%
## [10] target + quadrant + target:quadrant + participant : 5.768033e+23 ±2.65%
## [11] target + block + quadrant + target:quadrant + participant : 2.650457e+38 ±2.26%
## [12] target + block + target:block + quadrant + target:quadrant + participant : 2.9503e+38 ±3.11%
## [13] block + quadrant + block:quadrant + participant : 3.273786e+15 ±1.57%
## [14] target + block + quadrant + block:quadrant + participant : 1.247949e+40 ±3.29%
## [15] target + block + target:block + quadrant + block:quadrant + participant : 1.38838e+40 ±2.6%
## [16] target + block + quadrant + target:quadrant + block:quadrant + participant : 5.093777e+38 ±3.04%
## [17] target + block + target:block + quadrant + target:quadrant + block:quadrant + participant : 5.619516e+38 ±2.68%
## [18] target + block + target:block + quadrant + target:quadrant + block:quadrant + target:block:quadrant + participant : 9.936863e+38 ±3.08%
##
## Against denominator:
## movementtime ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 1.00 2.30e+24
## block 0.74 1.00 9.84e+14
## block:target 0.32 0.53 2.46
## quadrant 0.74 1.00 1.64e+04
## quadrant:target 0.32 0.06 0.144
## block:quadrant 0.32 0.67 4.45
## block:quadrant:target 0.05 0.02 0.433
##
## * Compared among: all models
## * Priors odds: uniform-equal#Quadrant 1 vs Quadrant 2
MTANOVA2Quads(quadrantA= '1', quadrantB = '2')## Quadrants 1 and 2:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 target 2 94 19.6478858 7.424028e-08 * 0.0558009031
## 3 block 2 94 24.2867969 3.141750e-09 * 0.0431194111
## 4 quadrant 1 47 20.5600387 3.982181e-05 * 0.0217351641
## 5 target:block 4 188 4.8752397 9.197791e-04 * 0.0176937540
## 6 target:quadrant 2 94 0.6347070 5.323471e-01 0.0008415847
## 7 block:quadrant 2 94 3.6058248 3.098671e-02 * 0.0052323922
## 8 target:block:quadrant 4 188 0.5238989 7.182822e-01 0.0011924901
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 2 target 0.73177709 7.598232e-04 *
## 3 block 0.53292188 5.167276e-07 *
## 5 target:block 0.02977641 1.152434e-29 *
## 6 target:quadrant 0.58384301 4.215121e-06 *
## 7 block:quadrant 0.99027703 7.987378e-01
## 8 target:block:quadrant 0.16620590 8.729295e-14 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 2 target 0.7885049 1.206472e-06 * 0.8112244 8.935972e-07
## 3 block 0.6816270 5.513631e-07 * 0.6950122 4.433437e-07
## 5 target:block 0.3561927 1.930860e-02 * 0.3641726 1.857997e-02
## 6 target:quadrant 0.7061364 4.804647e-01 0.7215659 4.836685e-01
## 7 block:quadrant 0.9903707 3.142424e-02 * 1.0337307 3.098671e-02
## 8 target:block:quadrant 0.5009273 5.942557e-01 0.5232545 6.020227e-01
## p[HF]<.05
## 2 *
## 3 *
## 5 *
## 6
## 7 *
## 8MTBayesANOVA2Quads(quadrantA= '1', quadrantB = '2')## Quadrants 1 and 2:
## Bayes factor analysis
## --------------
## [1] target + participant : 45600883613 ±1.18%
## [2] block + participant : 37558680 ±0.66%
## [3] target + block + participant : 8.892186e+18 ±1.16%
## [4] target + block + target:block + participant : 2.233835e+20 ±1.78%
## [5] quadrant + participant : 3484.774 ±0.96%
## [6] target + quadrant + participant : 3.505301e+14 ±1.58%
## [7] block + quadrant + participant : 237858310091 ±1.39%
## [8] target + block + quadrant + participant : 1.396814e+23 ±1.85%
## [9] target + block + target:block + quadrant + participant : 4.607053e+24 ±1.83%
## [10] target + quadrant + target:quadrant + participant : 1.378902e+13 ±3%
## [11] target + block + quadrant + target:quadrant + participant : 5.857218e+21 ±5.24%
## [12] target + block + target:block + quadrant + target:quadrant + participant : 1.779602e+23 ±2.13%
## [13] block + quadrant + block:quadrant + participant : 84932425081 ±3.33%
## [14] target + block + quadrant + block:quadrant + participant : 6.117168e+22 ±4.1%
## [15] target + block + target:block + quadrant + block:quadrant + participant : 2.054504e+24 ±2.77%
## [16] target + block + quadrant + target:quadrant + block:quadrant + participant : 2.501675e+21 ±5.96%
## [17] target + block + target:block + quadrant + target:quadrant + block:quadrant + participant : 7.973709e+22 ±2.8%
## [18] target + block + target:block + quadrant + target:quadrant + block:quadrant + target:block:quadrant + participant : 1.644841e+21 ±3.22%
##
## Against denominator:
## movementtime ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 1.00 7.89e+12
## block 0.74 1.00 6.99e+09
## block:target 0.32 0.97 71.67
## quadrant 0.74 1.00 1.10e+04
## quadrant:target 0.32 0.04 0.085
## block:quadrant 0.32 0.31 0.967
## block:quadrant:target 0.05 2.31e-04 0.004
##
## * Compared among: all models
## * Priors odds: uniform-equal#Quadrant 1 vs Switch hands, Quadrant 1
MTANOVA2Quads(quadrantA= '1', quadrantB = '1L')## Quadrants 1 and 1L:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 target 2 94 31.228121466 3.986052e-11 * 6.648657e-02
## 3 block 2 94 28.027641653 2.839216e-10 * 5.310798e-02
## 4 quadrant 1 47 0.007744007 9.302505e-01 7.801042e-06
## 5 target:block 4 188 9.134150454 9.160490e-07 * 2.130088e-02
## 6 target:quadrant 2 94 0.110594936 8.954177e-01 1.758673e-04
## 7 block:quadrant 2 94 1.825725660 1.667670e-01 2.770613e-03
## 8 target:block:quadrant 4 188 0.271193702 8.962673e-01 8.281075e-04
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 2 target 0.9011893 9.136253e-02
## 3 block 0.9869213 7.387511e-01
## 5 target:block 0.4868147 1.527995e-04 *
## 6 target:quadrant 0.6718101 1.063334e-04 *
## 7 block:quadrant 0.8466758 2.175177e-02 *
## 8 target:block:quadrant 0.3031620 1.783586e-08 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 2 target 0.9100748 2.498143e-10 * 0.9447484 1.230683e-10
## 3 block 0.9870902 3.605003e-10 * 1.0300829 2.839216e-10
## 5 target:block 0.7313412 1.785793e-05 * 0.7851314 9.829589e-06
## 6 target:quadrant 0.7529044 8.390424e-01 0.7723933 8.445759e-01
## 7 block:quadrant 0.8670589 1.723294e-01 0.8973387 1.710928e-01
## 8 target:block:quadrant 0.6233728 8.096804e-01 0.6610694 8.215406e-01
## p[HF]<.05
## 2 *
## 3 *
## 5 *
## 6
## 7
## 8MTBayesANOVA2Quads(quadrantA= '1', quadrantB = '1L')## Quadrants 1 and 1L:
## Bayes factor analysis
## --------------
## [1] target + participant : 1.427055e+14 ±3.48%
## [2] block + participant : 38792127974 ±1.32%
## [3] target + block + participant : 9.40096e+25 ±2.91%
## [4] target + block + target:block + participant : 4.36649e+28 ±2.2%
## [5] quadrant + participant : 0.08412092 ±8.07%
## [6] target + quadrant + participant : 1.061778e+13 ±4.39%
## [7] block + quadrant + participant : 2868597322 ±2.25%
## [8] target + block + quadrant + participant : 7.224314e+24 ±4.25%
## [9] target + block + target:block + quadrant + participant : 3.330258e+27 ±7.1%
## [10] target + quadrant + target:quadrant + participant : 285822381684 ±1.71%
## [11] target + block + quadrant + target:quadrant + participant : 2.042252e+23 ±5.04%
## [12] target + block + target:block + quadrant + target:quadrant + participant : 9.126583e+25 ±2.39%
## [13] block + quadrant + block:quadrant + participant : 316154876 ±3.38%
## [14] target + block + quadrant + block:quadrant + participant : 8.323949e+23 ±1.72%
## [15] target + block + target:block + quadrant + block:quadrant + participant : 2.250064e+27 ±81.85%
## [16] target + block + quadrant + target:quadrant + block:quadrant + participant : 2.693586e+22 ±7.06%
## [17] target + block + target:block + quadrant + target:quadrant + block:quadrant + participant : 1.166776e+25 ±2.42%
## [18] target + block + target:block + quadrant + target:quadrant + block:quadrant + target:block:quadrant + participant : 1.970759e+23 ±4.85%
##
## Against denominator:
## movementtime ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 1.00 4.21e+17
## block 0.74 1.00 1.15e+14
## block:target 0.32 1.00 1.05e+03
## quadrant 0.74 0.12 0.046
## quadrant:target 0.32 2.09e-03 0.005
## block:quadrant 0.32 0.05 0.104
## block:quadrant:target 0.05 3.99e-06 7.17e-05
##
## * Compared among: all models
## * Priors odds: uniform-equalIn comparing quadrants 1 and 4, We find a significant target x block x quadrant interaction.
Q1and4MTComparisonsEffSize()## contrast estimate SE df t.ratio p.value
## Q1 vs Q4, first block, Far -0.6105 0.1957 47 -3.120 0.0278
## Q1 vs Q4, second block, Far -0.3818 0.1422 47 -2.685 0.0898
## Q1 vs Q4, last block, Far 0.0278 0.0837 47 0.332 1.0000
## Q1 vs Q4, first block, Mid -0.8236 0.3586 47 -2.297 0.2353
## Q1 vs Q4, second block, Mid -0.4296 0.2904 47 -1.479 1.0000
## Q1 vs Q4, last block, Mid 0.3079 0.1568 47 1.964 0.4988
## Q1 vs Q4, first block, Near -0.1587 0.2419 47 -0.656 1.0000
## Q1 vs Q4, second block, Near -0.7693 0.2548 47 -3.019 0.0368
## Q1 vs Q4, last block, Near -0.5006 0.1964 47 -2.549 0.1273
##
## P value adjustment: bonferroni method for 9 tests
## contrast etasquared
## 1 Q1 vs Q4, first block, Far 0.171544216
## 2 Q1 vs Q4, second block, Far 0.133026922
## 3 Q1 vs Q4, last block, Far 0.002343253
## 4 Q1 vs Q4, first block, Mid 0.100893540
## 5 Q1 vs Q4, second block, Mid 0.044477939
## 6 Q1 vs Q4, last block, Mid 0.075864658
## 7 Q1 vs Q4, first block, Near 0.009075564
## 8 Q1 vs Q4, second block, Near 0.162389699
## 9 Q1 vs Q4, last block, Near 0.121422703Q1and4MTComparisonsBayesfollowup()## Bayesian t-test Quad 1 vs Quad 4, block 1, far target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 5.070574 ±0.01%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test Quad 1 vs Quad 4, block 2, far target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 1.050106 ±0.01%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test Quad 1 vs Quad 4, last block, far target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.2195581 ±0.02%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test Quad 1 vs Quad 4, block 1, mid target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 1.358812 ±0.01%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test Quad 1 vs Quad 4, block 2, mid target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.4515481 ±0.02%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test Quad 1 vs Quad 4, last block, mid target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.5761073 ±0.02%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test Quad 1 vs Quad 4, block 1, near target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.2422631 ±0.02%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test Quad 1 vs Quad 4, block 2, near target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 1.657446 ±0.01%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test Quad 1 vs Quad 4, last block, near target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 1.518271 ±0.01%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZSFollow-up tests show that the interaction is driven by a difference between quadrants for the far target in the first block, and a difference between quadrants for the near target in the second block. This is expected, given that we see slower completion times in the first few trials in quadrant 1 reaches.
In comparing quadrants 1 and 2, We find a significant block x quadrant interaction.
Q1and2MTComparisonsEffSize()## contrast estimate SE df t.ratio p.value
## Q1 vs Q2, first block -0.573 0.199 47 -2.879 0.0180
## Q1 vs Q2, second block -0.722 0.172 47 -4.197 0.0004
## Q1 vs Q2, last block -0.163 0.108 47 -1.502 0.4191
##
## P value adjustment: bonferroni method for 3 tests
## contrast etasquared
## 1 Q1 vs Q2, first block 0.14990805
## 2 Q1 vs Q2, second block 0.27260516
## 3 Q1 vs Q2, last block 0.04582408Q1and2MTComparisonsBayesfollowup()## Bayesian t-test Quad 1 vs Quad 2, block 1:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.944023 ±0.02%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test Quad 1 vs Quad 2, block 2:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 570.1504 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test Quad 1 vs Quad 2, last block,:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.345297 ±0.05%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZSFollow-up tests show that completion times in quadrant 1 are slower for the first two blocks than in quadrant 2. Finally, we do not find any quadrant main or interaction effects when comparing completion times after switching to the nondominant hand and those in quadrant 1. The shorter completion times for quadrants 4 and 2, compared to quadrant 1, is evidence that learning for reaches in the target locations has transferred to these new locations. Moreover, this learning is dependent on target distance from the mirror axis, where far targets showed faster completion times.
Completion times during washout trials
We have already shown that far targets have faster completion times for some blocks of washout trials, compared to the other targets. We can now compare these completion times with those during the aligned reaches. We conduct a 3x3x2 (target x block x session) within-subjects ANOVA.
RAEUntrainedHandMTANOVA()## Comparing completion times during washout trials with aligned trials across targets and blocks, untrained hand:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 block 2 94 35.349380 3.569140e-12 * 0.061259305
## 3 target 2 94 3.099120 4.972613e-02 * 0.004183635
## 4 session 1 47 0.941249 3.369233e-01 0.002077640
## 5 block:target 4 188 2.668055 3.370257e-02 * 0.006968396
## 6 block:session 2 94 4.794514 1.040549e-02 * 0.006285742
## 7 target:session 2 94 4.242103 1.722396e-02 * 0.004995036
## 8 block:target:session 4 188 1.682627 1.557123e-01 0.004288190
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 2 block 0.6264934 2.133432e-05 *
## 3 target 0.9292240 1.848289e-01
## 5 block:target 0.2342945 1.007310e-10 *
## 6 block:session 0.6449955 4.166817e-05 *
## 7 target:session 0.9819714 6.580725e-01
## 8 block:target:session 0.1568597 2.625269e-14 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 2 block 0.7280635 1.752889e-09 * 0.7453702 1.180576e-09
## 3 target 0.9339022 5.345557e-02 0.9710873 5.132483e-02
## 5 block:target 0.5991936 6.369228e-02 0.6336155 6.027661e-02
## 6 block:session 0.7380050 1.922094e-02 * 0.7561780 1.841797e-02
## 7 target:session 0.9822907 1.782039e-02 * 1.0247480 1.722396e-02
## 8 block:target:session 0.5284502 1.895111e-01 0.5539701 1.877372e-01
## p[HF]<.05
## 2 *
## 3
## 5
## 6 *
## 7 *
## 8RAEUntrainedHandMTBayesANOVA()## Comparing completion times during washout trials with aligned trials across targets and blocks, untrained hand:
## Bayes factor analysis
## --------------
## [1] target + participant : 0.136058 ±0.91%
## [2] block + participant : 5.565021e+14 ±0.96%
## [3] target + block + participant : 9.453785e+13 ±1.19%
## [4] target + block + target:block + participant : 1.701603e+13 ±1.74%
## [5] session + participant : 0.2467167 ±2.15%
## [6] target + session + participant : 0.03324752 ±1.82%
## [7] block + session + participant : 1.510942e+14 ±1.72%
## [8] target + block + session + participant : 2.866245e+13 ±7.11%
## [9] target + block + target:block + session + participant : 4.635246e+12 ±1.57%
## [10] target + session + target:session + participant : 0.01328863 ±2.25%
## [11] target + block + session + target:session + participant : 1.327956e+13 ±2.49%
## [12] target + block + target:block + session + target:session + participant : 2.569772e+12 ±5.43%
## [13] block + session + block:session + participant : 1.69147e+14 ±2.37%
## [14] target + block + session + block:session + participant : 3.075772e+13 ±3.83%
## [15] target + block + target:block + session + block:session + participant : 6.176481e+12 ±8.33%
## [16] target + block + session + target:session + block:session + participant : 1.535824e+13 ±2.55%
## [17] target + block + target:block + session + target:session + block:session + participant : 2.913988e+12 ±2.54%
## [18] target + block + target:block + session + target:session + block:session + target:block:session + participant : 508051120961 ±33.63%
##
## Against denominator:
## movementtime ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 0.20 0.088
## block 0.74 1.00 2.73e+14
## block:target 0.32 0.03 0.069
## session 0.74 0.39 0.227
## session:target 0.32 0.03 0.071
## block:session 0.32 0.21 0.561
## block:session:target 0.05 4.65e-04 0.008
##
## * Compared among: all models
## * Priors odds: uniform-equalWe do not find a session effect, but do find a block x session interaction. From the plots, we see that this is likely driven by how completion times in both sessions taper off a bit differently. However, the lack of a main effect suggests that completion times are not different between sessions.
Path Length
plotCtrlGenPL()
Learned performance
We first tested for target or block effects for path length within each quadrant. Thus, we conducted 3x3 (target x block) within-subjects ANOVA for quadrants 1, 4, 2, top-up trials in quadrant 1 (Quadrant 1A in tests below), quadrant 1 after switching hands (Quadrant 1L in tests below), and washout (Quadrant 1W).
pathlengthANOVA()## Quadrant 1:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 block 2 94 27.31672 4.441516e-10 * 0.08165414
## 3 target 2 94 18.90872 1.253963e-07 * 0.07077614
## 4 block:target 4 188 5.85361 1.842852e-04 * 0.04418483
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 2 block 0.9907862 8.082378e-01
## 3 target 0.9148337 1.290830e-01
## 4 block:target 0.3787548 1.383598e-06 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 2 block 0.9908704 5.237882e-10 * 1.0342865 4.441516e-10
## 3 target 0.9215177 3.387851e-07 * 0.9573905 2.150488e-07
## 4 block:target 0.7078015 1.103567e-03 * 0.7578761 8.104160e-04
## p[HF]<.05
## 2 *
## 3 *
## 4 *
##
## Quadrant 4:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 block 2 94 6.056626 3.356115e-03 * 0.02008565
## 3 target 2 94 31.543716 3.298841e-11 * 0.13096988
## 4 block:target 4 188 2.356535 5.523542e-02 0.01472088
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 2 block 0.9404363 2.435431e-01
## 3 target 0.8998320 8.824968e-02
## 4 block:target 0.4295296 1.512285e-05 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 2 block 0.9437847 4.038162e-03 * 0.9820279 3.560454e-03
## 3 target 0.9089521 2.151055e-10 * 0.9435087 1.055497e-10
## 4 block:target 0.7001630 7.899677e-02 0.7490569 7.449776e-02
## p[HF]<.05
## 2 *
## 3 *
## 4
##
## Quadrant 2:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 block 2 94 1.9846267 0.1431490840 0.006719568
## 3 target 2 94 9.3974966 0.0001902775 * 0.039714599
## 4 block:target 4 188 0.3116726 0.8699397792 0.001688372
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 2 block 0.9619957 0.41018676
## 3 target 0.9322035 0.19895149
## 4 block:target 0.6222413 0.01048157 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 2 block 0.9633871 0.1450010243 1.0037573 0.1431490840
## 3 target 0.9365081 0.0002755495 * 0.9739713 0.0002214478
## 4 block:target 0.8202500 0.8341429085 0.8891328 0.8491221316
## p[HF]<.05
## 2
## 3 *
## 4
##
## Quadrant 1A:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 block 2 94 5.980577 3.590172e-03 * 0.02123791
## 3 target 2 94 11.513620 3.369162e-05 * 0.04546399
## 4 block:target 4 188 2.951185 2.139821e-02 * 0.01225473
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 2 block 0.8464615 0.02162549 *
## 3 target 0.8626760 0.03345778 *
## 4 block:target 0.7622208 0.19555267
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 2 block 0.8668978 5.524292e-03 * 0.8971615 0.0050077253
## 3 target 0.8792569 8.253728e-05 * 0.9107643 0.0000653081
## 4 block:target 0.8794163 2.704241e-02 * 0.9592857 0.0231531467
## p[HF]<.05
## 2 *
## 3 *
## 4 *
##
## Quadrant 1L:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 block 2 94 12.011702 2.262073e-05 * 0.03196850
## 3 target 2 94 12.545807 1.481132e-05 * 0.05533743
## 4 block:target 4 188 2.914864 2.268748e-02 * 0.01873846
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 2 block 0.8531103 0.025889214 *
## 3 target 0.8835716 0.058017603
## 4 block:target 0.5781205 0.003118553 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 2 block 0.8719234 6.134533e-05 * 0.9026910 4.825487e-05
## 3 target 0.8957135 3.475569e-05 * 0.9289001 2.648633e-05
## 4 block:target 0.7802996 3.444247e-02 * 0.8421922 3.060117e-02
## p[HF]<.05
## 2 *
## 3 *
## 4 *
##
## Quadrant 1W:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 block 2 94 42.112765 8.738223e-14 * 0.14662772
## 3 target 2 94 7.165305 1.269706e-03 * 0.03057220
## 4 block:target 4 188 3.960081 4.138968e-03 * 0.03211978
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 2 block 0.24032861 5.734902e-15 *
## 3 target 0.70284587 3.004569e-04 *
## 4 block:target 0.05300854 2.783536e-24 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 2 block 0.5682879 7.932101e-09 * 0.5729581 7.006979e-09
## 3 target 0.7709184 3.285060e-03 * 0.7920268 3.008534e-03
## 4 block:target 0.5384969 1.956740e-02 * 0.5652198 1.785954e-02
## p[HF]<.05
## 2 *
## 3 *
## 4 *pathlengthBayesANOVA()## Quadrant 1:
## Bayes factor analysis
## --------------
## [1] target + participant : 181027.8 ±0.7%
## [2] block + participant : 3037405 ±0.99%
## [3] target + block + participant : 2.96989e+12 ±1.76%
## [4] target + block + target:block + participant : 6.815434e+14 ±2.7%
##
## Against denominator:
## pathlength ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.60 1.00 1.50e+08
## block 0.60 1.00 2.52e+09
## block:target 0.20 1.00 917.94
##
## * Compared among: all models
## * Priors odds: uniform-equalQuadrant 4:
## Bayes factor analysis
## --------------
## [1] target + participant : 5.161798e+13 ±0.64%
## [2] block + participant : 1.925931 ±0.62%
## [3] target + block + participant : 2.465863e+14 ±2.94%
## [4] target + block + target:block + participant : 7.312425e+13 ±2.72%
##
## Against denominator:
## pathlength ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.60 1.00 8.46e+13
## block 0.60 0.86 4.13
## block:target 0.20 0.20 0.981
##
## * Compared among: all models
## * Priors odds: uniform-equalQuadrant 2:
## Bayes factor analysis
## --------------
## [1] target + participant : 2569.926 ±0.81%
## [2] block + participant : 0.157141 ±0.87%
## [3] target + block + participant : 466.9608 ±3.03%
## [4] target + block + target:block + participant : 7.683817 ±1.61%
##
## Against denominator:
## pathlength ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.60 1.00 1.75e+03
## block 0.60 0.16 0.123
## block:target 0.20 2.52e-03 0.010
##
## * Compared among: all models
## * Priors odds: uniform-equalQuadrant 1A:
## Bayes factor analysis
## --------------
## [1] target + participant : 28644.3 ±0.77%
## [2] block + participant : 12.65025 ±2.18%
## [3] target + block + participant : 561548.4 ±1.4%
## [4] target + block + target:block + participant : 169863.9 ±1.33%
##
## Against denominator:
## pathlength ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.60 1.00 3.71e+04
## block 0.60 0.96 17.02
## block:target 0.20 0.22 1.15
##
## * Compared among: all models
## * Priors odds: uniform-equalQuadrant 1L:
## Bayes factor analysis
## --------------
## [1] target + participant : 48493.54 ±0.55%
## [2] block + participant : 73.02842 ±0.71%
## [3] target + block + participant : 6729655 ±0.91%
## [4] target + block + target:block + participant : 6045159 ±1.06%
##
## Against denominator:
## pathlength ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.60 1.00 1.15e+05
## block 0.60 1.00 175.62
## block:target 0.20 0.47 3.57
##
## * Compared among: all models
## * Priors odds: uniform-equalQuadrant 1W:
## Bayes factor analysis
## --------------
## [1] target + participant : 8.000165 ±0.74%
## [2] block + participant : 2.105772e+13 ±0.86%
## [3] target + block + participant : 5.016366e+14 ±1.69%
## [4] target + block + target:block + participant : 3.464025e+15 ±1.22%
##
## Against denominator:
## pathlength ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.60 0.99 125.55
## block 0.60 1.00 2.95e+14
## block:target 0.20 0.87 26.51
##
## * Compared among: all models
## * Priors odds: uniform-equalIn quadrants 1, top-up trials to quadrant 1 (1A), reaches to quadrant 1 after switching hands (1L), and washout (1W), we find significant target x block interactions. We know from the plot that path length decreases across blocks. Thus, it is more interesting to test for target differences across the blocks of trials.
#Quadrant 1
quadrant1PLComparisonsEffSize()## contrast estimate SE df t.ratio p.value
## 1st block: Far vs. Mid 0.3210 0.1045 47 3.070 0.0319
## 1st block: Far vs. Near -0.1055 0.0719 47 -1.468 1.0000
## 1st block: Mid vs. Near -0.4265 0.0792 47 -5.386 <.0001
## 2nd block: Far vs. Mid 0.2072 0.0452 47 4.587 0.0003
## 2nd block: Far vs. Near 0.0885 0.0414 47 2.140 0.3378
## 2nd block: Mid vs. Near -0.1187 0.0467 47 -2.544 0.1288
## last block: Far vs. Mid 0.1934 0.0445 47 4.347 0.0007
## last block: Far vs. Near 0.2172 0.0847 47 2.563 0.1228
## last block: Mid vs. Near 0.0238 0.0775 47 0.306 1.0000
##
## P value adjustment: bonferroni method for 9 tests
## contrast etasquared
## 1 1st block: Far vs. Mid 0.167076704
## 2 1st block: Far vs. Near 0.043832396
## 3 1st block: Mid vs. Near 0.381671425
## 4 2nd block: Far vs. Mid 0.309273147
## 5 2nd block: Far vs. Near 0.088824194
## 6 2nd block: Mid vs. Near 0.121031904
## 7 last block: Far vs. Mid 0.286725012
## 8 last block: Far vs. Near 0.122602734
## 9 last block: Mid vs. Near 0.001994775quadrant1PLComparisonsBayesfollowup()## Bayesian t-test block 1 far vs mid target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 12.60603 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test block 1 far vs near target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.5555968 ±0.02%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test block 1 mid vs near target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 1299.058 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test block 2 far vs mid target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 124.5808 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test block 2 far vs near target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 1.271848 ±0.01%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test block 2 mid vs near target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 1.843871 ±0.01%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test last block far vs mid target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 78.59169 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test last block far vs near target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 3.399239 ±0.01%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test last block mid vs near target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.2205006 ±0.02%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS#Quadrant 1A
quadrant1APLComparisonsEffSize()## contrast estimate SE df t.ratio p.value
## 1st block: Far vs. Mid 0.2005 0.0500 47 4.010 0.0019
## 1st block: Far vs. Near 0.0268 0.0357 47 0.749 1.0000
## 1st block: Mid vs. Near -0.1737 0.0544 47 -3.196 0.0224
## 2nd block: Far vs. Mid 0.0884 0.0479 47 1.848 0.6379
## 2nd block: Far vs. Near 0.0159 0.0303 47 0.524 1.0000
## 2nd block: Mid vs. Near -0.0726 0.0401 47 -1.808 0.6927
## last block: Far vs. Mid 0.1186 0.0347 47 3.416 0.0119
## last block: Far vs. Near 0.0961 0.0340 47 2.827 0.0619
## last block: Mid vs. Near -0.0225 0.0336 47 -0.671 1.0000
##
## P value adjustment: bonferroni method for 9 tests
## contrast etasquared
## 1 1st block: Far vs. Mid 0.254928590
## 2 1st block: Far vs. Near 0.011795225
## 3 1st block: Mid vs. Near 0.178509271
## 4 2nd block: Far vs. Mid 0.067749147
## 5 2nd block: Far vs. Near 0.005805544
## 6 2nd block: Mid vs. Near 0.065046002
## 7 last block: Far vs. Mid 0.198902991
## 8 last block: Far vs. Near 0.145333615
## 9 last block: Mid vs. Near 0.009490253quadrant1APLComparisonsBayesfollowup()## Bayesian t-test block 1 far vs mid target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 7.197919 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test block 1 far vs near target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.237635 ±0.02%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test block 1 mid vs near target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 2.463432 ±0.01%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test block 2 far vs mid target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.7020362 ±0.02%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test block 2 far vs near target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.2291583 ±0.02%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test block 2 mid vs near target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.582391 ±0.02%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test last block far vs mid target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 11.15562 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test last block far vs near target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 3.103705 ±0.01%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test last block mid vs near target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.2382996 ±0.02%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS#Quadrant 1L
quadrant1LPLComparisonsEffSize()## contrast estimate SE df t.ratio p.value
## 1st block: Far vs. Mid 0.33086 0.0747 47 4.430 0.0005
## 1st block: Far vs. Near -0.00818 0.0687 47 -0.119 1.0000
## 1st block: Mid vs. Near -0.33904 0.0736 47 -4.606 0.0003
## 2nd block: Far vs. Mid 0.31193 0.1155 47 2.702 0.0861
## 2nd block: Far vs. Near 0.19515 0.0816 47 2.391 0.1879
## 2nd block: Mid vs. Near -0.11679 0.1245 47 -0.938 1.0000
## last block: Far vs. Mid 0.17452 0.0545 47 3.200 0.0222
## last block: Far vs. Near 0.19729 0.0741 47 2.663 0.0952
## last block: Mid vs. Near 0.02277 0.0663 47 0.343 1.0000
##
## P value adjustment: bonferroni method for 9 tests
## contrast etasquared
## 1 1st block: Far vs. Mid 0.2945665889
## 2 1st block: Far vs. Near 0.0003022933
## 3 1st block: Mid vs. Near 0.3110508098
## 4 2nd block: Far vs. Mid 0.1344393459
## 5 2nd block: Far vs. Near 0.1084217702
## 6 2nd block: Mid vs. Near 0.0183858065
## 7 last block: Far vs. Mid 0.1788635096
## 8 last block: Far vs. Near 0.1310802914
## 9 last block: Mid vs. Near 0.0025041143quadrant1LPLComparisonsBayesfollowup()## Bayesian t-test block 1 far vs mid target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 17.45402 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test block 1 far vs near target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.2155901 ±0.02%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test block 1 mid vs near target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 94.64334 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test block 2 far vs mid target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 4.442139 ±0.01%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test block 2 far vs near target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 1.646917 ±0.01%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test block 2 mid vs near target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.3039183 ±0.02%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test last block far vs mid target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 11.94491 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test last block far vs near target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 3.595921 ±0.01%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test last block mid vs near target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.2218428 ±0.02%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS#Quadrant 1W
quadrant1WPLComparisonsEffSize()## contrast estimate SE df t.ratio p.value
## 1st block: Far vs. Mid 0.16054 0.0730 47 2.200 0.2946
## 1st block: Far vs. Near -0.05358 0.0539 47 -0.994 1.0000
## 1st block: Mid vs. Near -0.21412 0.0745 47 -2.874 0.0547
## 2nd block: Far vs. Mid 0.03874 0.0250 47 1.549 1.0000
## 2nd block: Far vs. Near -0.00342 0.0162 47 -0.211 1.0000
## 2nd block: Mid vs. Near -0.04216 0.0181 47 -2.332 0.2161
## last block: Far vs. Mid -0.01807 0.0176 47 -1.028 1.0000
## last block: Far vs. Near -0.03576 0.0170 47 -2.098 0.3719
## last block: Mid vs. Near -0.01769 0.0119 47 -1.489 1.0000
##
## P value adjustment: bonferroni method for 9 tests
## contrast etasquared
## 1 1st block: Far vs. Mid 0.0933863452
## 2 1st block: Far vs. Near 0.0205803151
## 3 1st block: Mid vs. Near 0.1494322489
## 4 2nd block: Far vs. Mid 0.0485636141
## 5 2nd block: Far vs. Near 0.0009453199
## 6 2nd block: Mid vs. Near 0.1037392704
## 7 last block: Far vs. Mid 0.0219776261
## 8 last block: Far vs. Near 0.0856211284
## 9 last block: Mid vs. Near 0.0450396887quadrant1WPLComparisonsBayesfollowup()## Bayesian t-test block 1 far vs mid target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 1.412268 ±0.01%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test block 1 far vs near target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.313237 ±0.02%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test block 1 mid vs near target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 6.127847 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test block 2 far vs mid target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.7192991 ±0.02%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test block 2 far vs near target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.2180624 ±0.02%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test block 2 mid vs near target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 1.611049 ±0.01%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test last block far vs mid target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.3078451 ±0.02%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test last block far vs near target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 1.085374 ±0.01%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test last block mid vs near target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.4352399 ±0.02%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZSIn quadrant 1, follow-up tests show that the path length for the far target is shorter compared to the middle target in all blocks, and that the middle target has a longer path length than near target in the first block.
In quadrant 1A (top-up trials), we find shorter path lengths for the far target compared to the middle target in the first and last block, while the path lengths for the middle target were longer that the near target in the first block.
In quadrant 1L (switch to nondominant hand), we find similar results as in quadrant 1A.
In quadrant 1W (washout trials), follow up frequentist tests did not show any significant results. But, Bayesian tests show that the middle target is different than the near target in the first block.
Taken together, it seems that movement trajectories were shortest for the far target and longest for the middle target.
For quadrant 4, we observe main effects of target and block. For quadrant 2, we observe a main effect of target. We conduct follow-up tests on the target effect.
#quadrant 4
quadrant4PLComparisonsEffSizeTargetEffect()## contrast estimate SE df t.ratio p.value
## Far vs. Mid 0.2635 0.0366 47 7.195 <.0001
## Far vs. Near 0.0953 0.0278 47 3.426 0.0038
## Mid vs. Near -0.1682 0.0357 47 -4.718 0.0001
##
## P value adjustment: bonferroni method for 3 tests
## contrast etasquared
## 1 Far vs. Mid 0.5241158
## 2 Far vs. Near 0.1998185
## 3 Mid vs. Near 0.3214198quadrant4PLComparisonsTargetEffectBayesfollowup()## Bayesian t-test far vs mid target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 154071.5 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test far vs near target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 7.410766 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test mid vs near target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 39.19806 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS#quadrant 2
quadrant2PLComparisonsEffSizeTargetEffect()## contrast estimate SE df t.ratio p.value
## Far vs. Mid 0.1418 0.0316 47 4.490 0.0001
## Far vs. Near 0.0546 0.0370 47 1.476 0.4399
## Mid vs. Near -0.0872 0.0300 47 -2.905 0.0168
##
## P value adjustment: bonferroni method for 3 tests
## contrast etasquared
## 1 Far vs. Mid 0.3001642
## 2 Far vs. Near 0.0442951
## 3 Mid vs. Near 0.1521891quadrant2PLComparisonsTargetEffectBayesfollowup()## Bayesian t-test far vs mid target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 28.6531 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test far vs near target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.4193616 ±0.02%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test mid vs near target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.8460889 ±0.01%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZSIn both quadrants, the target effect is accounted for by shorter path lengths for the far and near targets, compared to the middle target. Thus, path lengths support findings for completion times, where movements are faster and shorter for the far target, and slower and longer for the middle target.
Retention
To quantify retention, we compare the path lengths between the last block of mirror reversed reaches in session 1, with the first block of mirror reversed reaches in session 2.
retentionPLANOVA()## Comparing path length between part 1 and part 2 during learning, trained hand:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 target 2 94 18.189190 2.100616e-07 * 0.10646047
## 3 session 1 47 29.027428 2.242838e-06 * 0.06512149
## 4 target:session 2 94 9.932946 1.220415e-04 * 0.04565246
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 2 target 0.9090956 0.1116912797
## 4 target:session 0.7201432 0.0005255741 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 2 target 0.9166706 5.793392e-07 * 0.9520338 3.765784e-07
## 4 target:session 0.7813374 4.788498e-04 * 0.8033967 4.169628e-04
## p[HF]<.05
## 2 *
## 4 *retentionPLBayesANOVA()## Comparing path lengths between part 1 and part 2 during learning, trained hand:
## Bayes factor analysis
## --------------
## [1] target + participant : 508291.7 ±0.88%
## [2] session + participant : 1930.877 ±0.94%
## [3] target + session + participant : 4113517366 ±1.1%
## [4] target + session + target:session + participant : 475781718962 ±3.89%
##
## Against denominator:
## pathlength ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.60 1.00 1.66e+08
## session 0.60 1.00 6.29e+05
## session:target 0.20 0.99 462.59
##
## * Compared among: all models
## * Priors odds: uniform-equalWe find a significant target x session interaction.
part1and2PLComparisonsEffSize()## contrast estimate SE df t.ratio p.value
## Far: Part 1 vs Part 2 0.2392 0.0566 47 4.228 0.0003
## Mid: Part 1 vs Part 2 0.3418 0.0758 47 4.510 0.0001
## Near: Part 1 vs Part 2 -0.0237 0.0422 47 -0.562 1.0000
##
## P value adjustment: bonferroni method for 3 tests
## contrast etasquared
## 1 Far: Part 1 vs Part 2 0.275547535
## 2 Mid: Part 1 vs Part 2 0.302062210
## 3 Near: Part 1 vs Part 2 0.006682688part1and2PLComparisonsBayesfollowup()## Bayesian t-test part 1 far vs block 1 far:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 51.05797 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test part 1 mid vs block 1 mid:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 66.09445 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test part 1 near vs block 1 near:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.2353186 ±0.02%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZSFollow-up tests show that the far and middle targets had slightly longer path lengths for the first block in session 2, compared to the last block in session 1. However, in comparing path length plots, we see that the starting path lengths in session 2 are shorter than how participants started in session 1, suggesting that there was retention of learning.
Generalization across the workspace and hands
To quantify generalization, we compare path length across quadrants. We conduct a 3x3x2 (target x block x quadrant) within-subjects ANOVA to compare the first set of reaches to quadrant 1 with reaches in quadrant 4. We repeat this test but instead compare quadrant 1 with quadrant 2, quadrant 1 and reaches to quadrant 1 after switching hands (Quadrant 1L).
#Quadrant 1 vs Quadrant 4
PLANOVA2Quads(quadrantA= '1', quadrantB = '4')## Quadrants 1 and 4:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 target 2 94 45.1194287 1.836924e-14 * 0.0936102625
## 3 block 2 94 29.9560713 8.613578e-11 * 0.0472125883
## 4 quadrant 1 47 8.1495336 6.390070e-03 * 0.0090243153
## 5 target:block 4 188 7.3758953 1.539295e-05 * 0.0244977684
## 6 target:quadrant 2 94 0.1774823 8.376558e-01 0.0003575667
## 7 block:quadrant 2 94 8.5839316 3.766899e-04 * 0.0139527356
## 8 target:block:quadrant 4 188 2.4459802 4.796576e-02 * 0.0094940932
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 2 target 0.8991779 8.678600e-02
## 3 block 0.9935590 8.618956e-01
## 5 target:block 0.6680599 3.175772e-02 *
## 6 target:quadrant 0.8965993 8.123869e-02
## 7 block:quadrant 0.9286346 1.821511e-01
## 8 target:block:quadrant 0.2734334 2.276590e-09 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 2 target 0.9084120 2.364596e-13 * 0.9429124 9.028390e-14
## 3 block 0.9936003 9.767824e-11 * 1.0373230 8.613578e-11
## 5 target:block 0.8225118 6.827605e-05 * 0.8918007 3.812063e-05
## 6 target:quadrant 0.9062891 8.167966e-01 0.9405687 8.247816e-01
## 7 block:quadrant 0.9333884 5.332096e-04 * 0.9705188 4.392711e-04
## 8 target:block:quadrant 0.6698903 7.377831e-02 0.7142243 6.960860e-02
## p[HF]<.05
## 2 *
## 3 *
## 5 *
## 6
## 7 *
## 8PLBayesANOVA2Quads(quadrantA= '1', quadrantB = '4')## Quadrants 1 and 4:
## Bayes factor analysis
## --------------
## [1] target + participant : 5.273775e+17 ±0.81%
## [2] block + participant : 16033719 ±0.72%
## [3] target + block + participant : 1.112168e+26 ±2.49%
## [4] target + block + target:block + participant : 3.325868e+28 ±3.21%
## [5] quadrant + participant : 3.352745 ±0.82%
## [6] target + quadrant + participant : 2.712887e+18 ±0.97%
## [7] block + quadrant + participant : 72976984 ±6.12%
## [8] target + block + quadrant + participant : 7.302929e+26 ±1.53%
## [9] target + block + target:block + quadrant + participant : 2.518184e+29 ±2%
## [10] target + quadrant + target:quadrant + participant : 9.211263e+16 ±6.93%
## [11] target + block + quadrant + target:quadrant + participant : 2.428356e+25 ±8.24%
## [12] target + block + target:block + quadrant + target:quadrant + participant : 7.804269e+27 ±2.7%
## [13] block + quadrant + block:quadrant + participant : 731573055 ±2.89%
## [14] target + block + quadrant + block:quadrant + participant : 1.683615e+28 ±2.8%
## [15] target + block + target:block + quadrant + block:quadrant + participant : 6.910697e+30 ±2.04%
## [16] target + block + quadrant + target:quadrant + block:quadrant + participant : 4.957677e+26 ±2.68%
## [17] target + block + target:block + quadrant + target:quadrant + block:quadrant + participant : 2.315114e+29 ±4.93%
## [18] target + block + target:block + quadrant + target:quadrant + block:quadrant + target:block:quadrant + participant : 1.457302e+29 ±4.54%
##
## Against denominator:
## pathlength ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 1.00 3.31e+21
## block 0.74 1.00 8.14e+11
## block:target 0.32 1.00 902.59
## quadrant 0.74 1.00 80.97
## quadrant:target 0.32 0.05 0.116
## block:quadrant 0.32 0.96 53.88
## block:quadrant:target 0.05 0.02 0.352
##
## * Compared among: all models
## * Priors odds: uniform-equal#Quadrant 1 vs Quadrant 2
PLANOVA2Quads(quadrantA= '1', quadrantB = '2')## Quadrants 1 and 2:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 target 2 94 23.420507 5.581352e-09 * 0.055285548
## 3 block 2 94 24.552843 2.637153e-09 * 0.037450330
## 4 quadrant 1 47 7.208682 9.991124e-03 * 0.008982951
## 5 target:block 4 188 3.836525 5.067925e-03 * 0.015143355
## 6 target:quadrant 2 94 2.659401 7.525407e-02 0.004423675
## 7 block:quadrant 2 94 10.904214 5.510884e-05 * 0.018500573
## 8 target:block:quadrant 4 188 4.728479 1.170949e-03 * 0.013767298
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 2 target 0.9354853 0.2156998944
## 3 block 0.9679733 0.4729961578
## 5 target:block 0.6002782 0.0058425106 *
## 6 target:quadrant 0.8971331 0.0823584881
## 7 block:quadrant 0.9861812 0.7261135536
## 8 target:block:quadrant 0.4843176 0.0001391832 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 2 target 0.9393952 1.439677e-08 * 0.9771673 7.974919e-09
## 3 block 0.9689672 4.380336e-09 * 1.0099498 2.637153e-09
## 5 target:block 0.7921080 9.777978e-03 * 0.8560310 7.981184e-03
## 6 target:quadrant 0.9067277 8.099805e-02 0.9410530 7.883984e-02
## 7 block:quadrant 0.9863696 6.058987e-05 * 1.0292818 5.510884e-05
## 8 target:block:quadrant 0.7627273 3.365584e-03 * 0.8216532 2.585680e-03
## p[HF]<.05
## 2 *
## 3 *
## 5 *
## 6
## 7 *
## 8 *PLBayesANOVA2Quads(quadrantA= '1', quadrantB = '2')## Quadrants 1 and 2:
## Bayes factor analysis
## --------------
## [1] target + participant : 5720919528 ±0.72%
## [2] block + participant : 577719.7 ±1.31%
## [3] target + block + participant : 1.106676e+16 ±1.25%
## [4] target + block + target:block + participant : 4.115929e+16 ±2.12%
## [5] quadrant + participant : 4.407172 ±0.84%
## [6] target + quadrant + participant : 34101299035 ±1.52%
## [7] block + quadrant + participant : 3025839 ±2.1%
## [8] target + block + quadrant + participant : 8.660182e+16 ±3.6%
## [9] target + block + target:block + quadrant + participant : 3.385665e+17 ±3.35%
## [10] target + quadrant + target:quadrant + participant : 6744122361 ±2.01%
## [11] target + block + quadrant + target:quadrant + participant : 1.891001e+16 ±4.72%
## [12] target + block + target:block + quadrant + target:quadrant + participant : 7.434101e+16 ±4.36%
## [13] block + quadrant + block:quadrant + participant : 419552127 ±1.51%
## [14] target + block + quadrant + block:quadrant + participant : 2.062115e+19 ±1.44%
## [15] target + block + target:block + quadrant + block:quadrant + participant : 1.204951e+20 ±9.87%
## [16] target + block + quadrant + target:quadrant + block:quadrant + participant : 4.885046e+18 ±2.12%
## [17] target + block + target:block + quadrant + target:quadrant + block:quadrant + participant : 2.510405e+19 ±4.89%
## [18] target + block + target:block + quadrant + target:quadrant + block:quadrant + target:block:quadrant + participant : 1.312029e+20 ±3.4%
##
## Against denominator:
## pathlength ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 1.00 2.56e+11
## block 0.74 1.00 2.32e+09
## block:target 0.32 0.92 23.44
## quadrant 0.74 1.00 2.07e+03
## quadrant:target 0.32 0.53 2.47
## block:quadrant 0.32 1.00 1.15e+03
## block:quadrant:target 0.05 0.43 13.76
##
## * Compared among: all models
## * Priors odds: uniform-equal#Quadrant 1 vs Switch hands, Quadrant 1
PLANOVA2Quads(quadrantA= '1', quadrantB = '1L')## Quadrants 1 and 1L:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 target 2 94 24.7897660 2.257668e-09 * 0.0606153494
## 3 block 2 94 35.2737660 3.726616e-12 * 0.0488760281
## 4 quadrant 1 47 4.1047632 4.845983e-02 * 0.0053485819
## 5 target:block 4 188 7.9240972 6.348866e-06 * 0.0276348466
## 6 target:quadrant 2 94 0.4986625 6.089399e-01 0.0009049771
## 7 block:quadrant 2 94 2.2927179 1.066128e-01 0.0034034534
## 8 target:block:quadrant 4 188 0.3577068 8.384454e-01 0.0012465698
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 2 target 0.9817035 0.6539542960
## 3 block 0.9910791 0.8137508652
## 5 target:block 0.7791385 0.2538264849
## 6 target:quadrant 0.7293800 0.0007045934 *
## 7 block:quadrant 0.8424460 0.0193850754 *
## 8 target:block:quadrant 0.7182029 0.0902601799
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 2 target 0.9820322 3.036723e-09 * 1.0244607 2.257668e-09
## 3 block 0.9911580 4.554898e-12 * 1.0346064 3.726616e-12
## 5 target:block 0.8842846 1.842588e-05 * 0.9650921 8.751651e-06
## 6 target:quadrant 0.7870174 5.650900e-01 0.8095994 5.702460e-01
## 7 block:quadrant 0.8638906 1.147656e-01 0.8938539 1.129395e-01
## 8 target:block:quadrant 0.8763852 8.139150e-01 0.9556732 8.301471e-01
## p[HF]<.05
## 2 *
## 3 *
## 5 *
## 6
## 7
## 8PLBayesANOVA2Quads(quadrantA= '1', quadrantB = '1L')## Quadrants 1 and 1L:
## Bayes factor analysis
## --------------
## [1] target + participant : 112184424741 ±4.07%
## [2] block + participant : 202302066 ±0.65%
## [3] target + block + participant : 1.395349e+20 ±3.81%
## [4] target + block + target:block + participant : 3.406679e+23 ±1.3%
## [5] quadrant + participant : 0.8375966 ±1.55%
## [6] target + quadrant + participant : 113772069570 ±3.91%
## [7] block + quadrant + participant : 197835835 ±1.32%
## [8] target + block + quadrant + participant : 1.688357e+20 ±2.02%
## [9] target + block + target:block + quadrant + participant : 4.403082e+23 ±1.78%
## [10] target + quadrant + target:quadrant + participant : 4515164913 ±4.47%
## [11] target + block + quadrant + target:quadrant + participant : 6.960374e+18 ±4.15%
## [12] target + block + target:block + quadrant + target:quadrant + participant : 1.884329e+22 ±4.03%
## [13] block + quadrant + block:quadrant + participant : 24361250 ±2.53%
## [14] target + block + quadrant + block:quadrant + participant : 2.274653e+19 ±2.58%
## [15] target + block + target:block + quadrant + block:quadrant + participant : 6.873276e+22 ±3.98%
## [16] target + block + quadrant + target:quadrant + block:quadrant + participant : 8.697957e+17 ±1.98%
## [17] target + block + target:block + quadrant + target:quadrant + block:quadrant + participant : 2.934744e+21 ±6.43%
## [18] target + block + target:block + quadrant + target:quadrant + block:quadrant + target:block:quadrant + participant : 6.919835e+19 ±19.91%
##
## Against denominator:
## pathlength ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 1.00 7.34e+14
## block 0.74 1.00 1.35e+12
## block:target 0.32 1.00 5.57e+03
## quadrant 0.74 0.61 0.557
## quadrant:target 0.32 0.03 0.056
## block:quadrant 0.32 0.08 0.194
## block:quadrant:target 0.05 7.94e-05 0.001
##
## * Compared among: all models
## * Priors odds: uniform-equalIn comparing quadrants 1 and 4, We find a significant block x quadrant interaction.
Q1and4PLComparisonsEffSize()## contrast estimate SE df t.ratio p.value
## Q1 vs Q4, first block -0.17052 0.0362 47 -4.708 0.0001
## Q1 vs Q4, second block 0.00916 0.0258 47 0.355 1.0000
## Q1 vs Q4, last block -0.02582 0.0396 47 -0.652 1.0000
##
## P value adjustment: bonferroni method for 3 tests
## contrast etasquared
## 1 Q1 vs Q4, first block 0.320440221
## 2 Q1 vs Q4, second block 0.002670466
## 3 Q1 vs Q4, last block 0.008963343Q1and4PLComparisonsBayesfollowup()## Bayesian t-test Quad 1 vs Quad 4, block 1:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 34.80642 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test Quad 1 vs Quad 4, block 2:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.1343048 ±0.1%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test Quad 1 vs Quad 4, last block,:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.1590368 ±0.09%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZSFollow-up tests show that the interaction is driven by a difference between quadrants in the first block. This is expected, given that we see longer path lengths in the first few trials in quadrant 1 reaches.
In comparing quadrants 1 and 2, We find a significant target x block x quadrant interaction.
Q1and2PLComparisonsEffSize()## contrast estimate SE df t.ratio p.value
## Q1 vs Q2, first block, Far -0.17481 0.0725 47 -2.412 0.1783
## Q1 vs Q2, second block, Far 0.04102 0.0437 47 0.940 1.0000
## Q1 vs Q2, last block, Far 0.05633 0.0320 47 1.759 0.7652
## Q1 vs Q2, first block, Mid -0.37265 0.0720 47 -5.175 <.0001
## Q1 vs Q2, second block, Mid -0.00744 0.0495 47 -0.150 1.0000
## Q1 vs Q2, last block, Mid 0.00642 0.0507 47 0.127 1.0000
## Q1 vs Q2, first block, Near -0.02439 0.0516 47 -0.473 1.0000
## Q1 vs Q2, second block, Near -0.01080 0.0474 47 -0.228 1.0000
## Q1 vs Q2, last block, Near -0.07877 0.0806 47 -0.978 1.0000
##
## P value adjustment: bonferroni method for 9 tests
## contrast etasquared
## 1 Q1 vs Q2, first block, Far 0.1101639253
## 2 Q1 vs Q2, second block, Far 0.0184364558
## 3 Q1 vs Q2, last block, Far 0.0617899003
## 4 Q1 vs Q2, first block, Mid 0.3629994754
## 5 Q1 vs Q2, second block, Mid 0.0004812673
## 6 Q1 vs Q2, last block, Mid 0.0003410922
## 7 Q1 vs Q2, first block, Near 0.0047334875
## 8 Q1 vs Q2, second block, Near 0.0011033106
## 9 Q1 vs Q2, last block, Near 0.0199289480Q1and2PLComparisonsBayesfollowup()## Bayesian t-test Quad 1 vs Quad 2, block 1, far target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 2.645761 ±0.01%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test Quad 1 vs Quad 2, block 2, far target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.2892594 ±0.02%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test Quad 1 vs Quad 2, last block, far target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.5891591 ±0.02%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test Quad 1 vs Quad 2, block 1, mid target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 154.8204 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test Quad 1 vs Quad 2, block 2, mid target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.2158622 ±0.02%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test Quad 1 vs Quad 2, last block, mid target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.2155251 ±0.02%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test Quad 1 vs Quad 2, block 1, near target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.2328805 ±0.02%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test Quad 1 vs Quad 2, block 2, near target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.2183228 ±0.02%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test Quad 1 vs Quad 2, last block, near target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.2947548 ±0.02%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZSFollow-up tests show that path lengths differ for the middle target between the two quadrants. We see in the plot that path lengths are longer in the first few trials of reaches in quadrant 1.
Finally, in comparing quadrant 1 with reaches using the nondominant hand, we find a main effect of quadrant but no interactions. From the plot it is evident that path lengths for the nondominant hand are longer on average, compared to those in quadrant 1.
Path lengths during washout trials
We have already shown that in washout trials, theere are longer path lengths to the middle target than the near target during the first block. We now compare path lengths with those during the aligned reaches. We conduct a 3x3x2 (target x block x session) within-subjects ANOVA.
RAEUntrainedHandPLANOVA()## Comparing path length during washout trials with aligned trials across targets and blocks, untrained hand:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 block 2 94 38.924818 4.841993e-13 * 0.072606406
## 3 target 2 94 5.460907 5.705807e-03 * 0.012190707
## 4 session 1 47 8.414360 5.646754e-03 * 0.014015147
## 5 block:target 4 188 3.351437 1.118984e-02 * 0.014117870
## 6 block:session 2 94 23.354652 5.832259e-09 * 0.042798755
## 7 target:session 2 94 4.840212 9.983003e-03 * 0.009994616
## 8 block:target:session 4 188 2.966849 2.086464e-02 * 0.011153314
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 2 block 0.5982875 7.394837e-06 *
## 3 target 0.9653238 4.440988e-01
## 5 block:target 0.2100331 1.084469e-11 *
## 6 block:session 0.8038496 6.592045e-03 *
## 7 target:session 0.8135940 8.697179e-03 *
## 8 block:target:session 0.2313415 7.784537e-11 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 2 block 0.7134131 5.806403e-10 * 0.7294604 3.900417e-10
## 3 target 0.9664860 6.274998e-03 * 1.0071959 5.705807e-03
## 5 block:target 0.6263848 2.848206e-02 * 0.6644977 2.586402e-02
## 6 block:session 0.8360153 7.542001e-08 * 0.8632359 4.928292e-08
## 7 target:session 0.8428818 1.449546e-02 * 0.8707711 1.356518e-02
## 8 block:target:session 0.6429799 4.227572e-02 * 0.6834199 3.899393e-02
## p[HF]<.05
## 2 *
## 3 *
## 5 *
## 6 *
## 7 *
## 8 *RAEUntrainedHandPLBayesANOVA()## Comparing path lengths during washout trials with aligned trials across targets and blocks, untrained hand:
## Bayes factor analysis
## --------------
## [1] target + participant : 1.574407 ±0.72%
## [2] block + participant : 678652333278 ±0.69%
## [3] target + block + participant : 1.760373e+12 ±11.14%
## [4] target + block + target:block + participant : 1.420108e+12 ±1.94%
## [5] session + participant : 21.42247 ±1.58%
## [6] target + session + participant : 34.92166 ±1.83%
## [7] block + session + participant : 2.42948e+13 ±6.56%
## [8] target + block + session + participant : 5.710002e+13 ±5.06%
## [9] target + block + target:block + session + participant : 5.097185e+13 ±1.59%
## [10] target + session + target:session + participant : 43.0591 ±1.68%
## [11] target + block + session + target:session + participant : 1.011079e+14 ±4.99%
## [12] target + block + target:block + session + target:session + participant : 9.735277e+13 ±4%
## [13] block + session + block:session + participant : 9.742465e+19 ±1.78%
## [14] target + block + session + block:session + participant : 3.708235e+20 ±15.68%
## [15] target + block + target:block + session + block:session + participant : 3.833597e+20 ±1.79%
## [16] target + block + session + target:session + block:session + participant : 6.651822e+20 ±2.68%
## [17] target + block + target:block + session + target:session + block:session + participant : 8.887196e+20 ±6%
## [18] target + block + target:block + session + target:session + block:session + target:block:session + participant : 7.353982e+20 ±2.5%
##
## Against denominator:
## pathlength ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 0.97 11.16
## block 0.74 1.00 1.10e+19
## block:target 0.32 0.64 3.84
## session 0.74 1.00 2.91e+08
## session:target 0.32 0.73 5.82
## block:session 0.32 1.00 2.03e+07
## block:session:target 0.05 0.23 5.50
##
## * Compared among: all models
## * Priors odds: uniform-equalWe find a main effect of session, and a significant target x block x session interaction. We conduct follow-up tests on the interaction.
untrainedHandSessionPLComparisonsEffSize()## contrast estimate SE df t.ratio
## Baseline vs Washout in part 2, first block, Far 0.10901 0.0517 47 2.108
## Baseline vs Washout in part 2, second block, Far -0.05528 0.0322 47 -1.715
## Baseline vs Washout in part 2, last block, Far 0.02476 0.0191 47 1.298
## Baseline vs Washout in part 2, first block, Mid 0.26889 0.0635 47 4.235
## Baseline vs Washout in part 2, second block, Mid 0.00391 0.0265 47 0.147
## Baseline vs Washout in part 2, last block, Mid 0.00858 0.0140 47 0.615
## Baseline vs Washout in part 2, first block, Near 0.07485 0.0413 47 1.812
## Baseline vs Washout in part 2, second block, Near -0.01107 0.0144 47 -0.768
## Baseline vs Washout in part 2, last block, Near -0.03485 0.0172 47 -2.028
## p.value
## 0.3632
## 0.8360
## 1.0000
## 0.0010
## 1.0000
## 1.0000
## 0.6877
## 1.0000
## 0.4342
##
## P value adjustment: bonferroni method for 9 tests
## contrast etasquared
## 1 Baseline vs Washout in part 2, first block, Far 0.0864085979
## 2 Baseline vs Washout in part 2, second block, Far 0.0589090249
## 3 Baseline vs Washout in part 2, last block, Far 0.0346083140
## 4 Baseline vs Washout in part 2, first block, Mid 0.2761811889
## 5 Baseline vs Washout in part 2, second block, Mid 0.0004614064
## 6 Baseline vs Washout in part 2, last block, Mid 0.0079808537
## 7 Baseline vs Washout in part 2, first block, Near 0.0652805394
## 8 Baseline vs Washout in part 2, second block, Near 0.0124026015
## 9 Baseline vs Washout in part 2, last block, Near 0.0804681557untrainedHandSessionPLComparisonsBayesfollowup()## Bayesian t-test baseline vs washout in part 2, block 1, far target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 1.346249 ±0.01%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test baseline vs washout in part 2, block 2, far target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.7490008 ±0.01%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test baseline vs washout in part 2, last block, far target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.4671051 ±0.02%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test baseline vs washout in part 2, block 1, mid target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 153.6851 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test baseline vs washout in part 2, block 2, mid target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.2163223 ±0.02%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test baseline vs washout in part 2, last block, mid target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.246922 ±0.02%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test baseline vs washout in part 2, block 1, near target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.7625263 ±0.01%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test baseline vs washout in part 2, block 2, near target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.2626931 ±0.02%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test baseline vs washout in part 2, last block, near target:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.8876418 ±0.01%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZSFollow-up tests show that the interaction is driven by the longer path lengths for the middle target during the first block of washout compared to the first block of aligned reaches. This confirms what we observe with the plots that path lengths for the middle target are longer during the first few trials of washout.
Study 2: Supplementary analyses for the online experiment
Given the large sample we were able to collect for the online study, we also investigate for any effects related to the device they used to control the cursor (either a mouse or trackpad), and for any effects related to the participants’ sex. Therefore, we split the data into mouse and trackpad users, and into males and females.
Session 1
Device used: Mouse vs. trackpad
Learning
plotDeviceCtrl()
We first plot angular reach deviations across trial types for each of the target locations. We observe large variability for the mouse users due to their sample being disproportionately lower than trackpad users (Mouse N = 19, Trackpad N = 44). However, we do not really see much of a difference in learning rates and asymptotes.
First, we test for an effect of device used in the two sets of aligned trials where participants either used their dominant or nondominant hand. We conduct a 3x3x2 mixed design ANOVA, with target and block as within-subjects factors and device as a between-subjects factor.
deviceAlignedLearningANOVA()## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Angular reach deviations during aligned trials across targets, blocks, and devices, trained hand:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 devices 1 61 3.0286463 0.08684903 0.005131584
## 3 block 2 122 0.3352930 0.71578539 0.001225883
## 5 target 2 122 3.5081228 0.03300968 * 0.013232738
## 4 devices:block 2 122 1.3520011 0.26257040 0.004924819
## 6 devices:target 2 122 0.3527732 0.70345100 0.001346699
## 7 block:target 4 244 1.0506891 0.38167776 0.007515510
## 8 devices:block:target 4 244 2.0164606 0.09276629 0.014324655
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.9895788 0.7303180
## 4 devices:block 0.9895788 0.7303180
## 5 target 0.9537018 0.2412003
## 6 devices:target 0.9537018 0.2412003
## 7 block:target 0.8399753 0.3222309
## 8 devices:block:target 0.8399753 0.3222309
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 block 0.9896863 0.71356152 1.0227026 0.71578539
## 4 devices:block 0.9896863 0.26254923 1.0227026 0.26257040
## 5 target 0.9557505 0.03511767 * 0.9859199 0.03366625
## 6 devices:target 0.9557505 0.69382427 0.9859199 0.70043877
## 7 block:target 0.9222250 0.37904686 0.9889524 0.38132794
## 8 devices:block:target 0.9222250 0.09868474 0.9889524 0.09358392
## p[HF]<.05
## 3
## 4
## 5 *
## 6
## 7
## 8## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Angular reach deviations during aligned trials across targets, blocks, and devices, untrained hand:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 devices 1 61 0.5155845 0.4754725 0.001285841
## 3 block 2 122 1.0882920 0.3400380 0.003317962
## 5 target 2 122 1.2473436 0.2909040 0.005089616
## 4 devices:block 2 122 0.3646288 0.6952086 0.001114131
## 6 devices:target 2 122 1.2705923 0.2843526 0.005183987
## 7 block:target 4 244 0.6116591 0.6546188 0.004103301
## 8 devices:block:target 4 244 1.8741660 0.1155651 0.012467209
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.9137101 0.0667194277
## 4 devices:block 0.9137101 0.0667194277
## 5 target 0.9955014 0.8734854864
## 6 devices:target 0.9955014 0.8734854864
## 7 block:target 0.5829693 0.0001954457 *
## 8 devices:block:target 0.5829693 0.0001954457 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 block 0.9205645 0.3362114 0.9478714 0.3375897
## 4 devices:block 0.9205645 0.6777227 0.9478714 0.6839087
## 5 target 0.9955215 0.2908269 1.0290359 0.2909040
## 6 devices:target 0.9955215 0.2842915 1.0290359 0.2843526
## 7 block:target 0.8050210 0.6195958 0.8551639 0.6293120
## 8 devices:block:target 0.8050210 0.1308638 0.8551639 0.1267539
## p[HF]<.05
## 3
## 4
## 5
## 6
## 7
## 8deviceAlignedLearningBayesANOVA()## Bayes factor analysis
## --------------
## [1] target + participant : 2.394597 ±0.94%
## [2] block + participant : 0.0223632 ±0.6%
## [3] target + block + participant : 0.05407954 ±0.98%
## [4] target + block + target:block + participant : 0.01085596 ±1.91%
## [5] devices + participant : 0.2922673 ±1.51%
## [6] target + devices + participant : 0.7084467 ±1.67%
## [7] block + devices + participant : 0.006697353 ±2.55%
## [8] target + block + devices + participant : 0.01582683 ±1.54%
## [9] target + block + target:block + devices + participant : 0.003149774 ±1.79%
## [10] target + devices + target:devices + participant : 0.04516488 ±3.13%
## [11] target + block + devices + target:devices + participant : 0.00101088 ±2.83%
## [12] target + block + target:block + devices + target:devices + participant : 0.0001949961 ±2.33%
## [13] block + devices + block:devices + participant : 0.001253784 ±26.82%
## [14] target + block + devices + block:devices + participant : 0.002478557 ±2.98%
## [15] target + block + target:block + devices + block:devices + participant : 0.0004704887 ±2.26%
## [16] target + block + devices + target:devices + block:devices + participant : 0.0001671219 ±10.62%
## [17] target + block + target:block + devices + target:devices + block:devices + participant : 3.310832e-05 ±5.7%
## [18] target + block + target:block + devices + target:devices + block:devices + target:block:devices + participant : 2.152358e-05 ±7.31%
##
## Against denominator:
## angdev ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 0.71 0.874
## block 0.74 0.03 0.010
## block:target 0.32 3.23e-03 0.007
## devices 0.74 0.24 0.110
## devices:target 0.32 0.01 0.022
## block:devices 0.32 9.70e-04 0.002
## block:devices:target 0.05 4.72e-06 8.50e-05
##
## * Compared among: all models
## * Priors odds: uniform-equalBayes factor analysis
## --------------
## [1] target + participant : 0.04216263 ±0.99%
## [2] block + participant : 0.07222589 ±1.15%
## [3] target + block + participant : 0.00308277 ±1.94%
## [4] target + block + target:block + participant : 9.502588e-05 ±1.73%
## [5] devices + participant : 0.1675481 ±1.09%
## [6] target + devices + participant : 0.006993133 ±1.68%
## [7] block + devices + participant : 0.01224428 ±1.61%
## [8] target + block + devices + participant : 0.0005174653 ±2.15%
## [9] target + block + target:block + devices + participant : 1.599333e-05 ±2.93%
## [10] target + devices + target:devices + participant : 0.001127933 ±1.42%
## [11] target + block + devices + target:devices + participant : 8.269996e-05 ±2%
## [12] target + block + target:block + devices + target:devices + participant : 2.633866e-06 ±2.65%
## [13] block + devices + block:devices + participant : 0.0007100751 ±1.71%
## [14] target + block + devices + block:devices + participant : 2.995828e-05 ±3.65%
## [15] target + block + target:block + devices + block:devices + participant : 1.02277e-06 ±8.98%
## [16] target + block + devices + target:devices + block:devices + participant : 5.983893e-06 ±12.8%
## [17] target + block + target:block + devices + target:devices + block:devices + participant : 1.598459e-07 ±2.86%
## [18] target + block + target:block + devices + target:devices + block:devices + target:block:devices + participant : 6.452285e-08 ±4.95%
##
## Against denominator:
## angdev ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 0.04 0.015
## block 0.74 0.07 0.026
## block:target 0.32 8.79e-05 1.91e-04
## devices 0.74 0.14 0.060
## devices:target 0.32 9.33e-04 0.002
## block:devices 0.32 5.72e-04 0.001
## block:devices:target 0.05 4.94e-08 8.89e-07
##
## * Compared among: all models
## * Priors odds: uniform-equalWe find no effects related to device used, suggestting that aligned reaches for both hands did not differ between mouse or trackpad users.
We then conducted the same 3x3x2 mixed design ANOVA during the mirror reversed trials.
devicemirrorANOVA()## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 devices 1 61 1.1566617 0.2863944 0.0018473042
## 3 target 2 122 1.7540801 0.1774026 0.0052519560
## 5 block 2 122 0.1222263 0.8850563 0.0004710773
## 4 devices:target 2 122 0.5014826 0.6068750 0.0015071600
## 6 devices:block 2 122 0.3151887 0.7302436 0.0012138787
## 7 target:block 4 244 0.3842324 0.8198233 0.0030367463
## 8 devices:target:block 4 244 0.1983549 0.9390675 0.0015699870
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 target 0.079907839 1.195863e-33 *
## 4 devices:target 0.079907839 1.195863e-33 *
## 5 block 0.781192494 6.063758e-04 *
## 6 devices:block 0.781192494 6.063758e-04 *
## 7 target:block 0.001261774 1.368065e-79 *
## 8 devices:target:block 0.001261774 1.368065e-79 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 target 0.5208083 0.1902924 0.5218639 0.1902894
## 4 devices:target 0.5208083 0.4887667 0.5218639 0.4891259
## 5 block 0.8204741 0.8456783 0.8401313 0.8506704
## 6 devices:block 0.8204741 0.6869185 0.8401313 0.6921489
## 7 target:block 0.4202281 0.6455762 0.4307912 0.6507600
## 8 devices:target:block 0.4202281 0.7821787 0.4307912 0.7877780
## p[HF]<.05
## 3
## 4
## 5
## 6
## 7
## 8devicemirrorBayesANOVA()## Bayes factor analysis
## --------------
## [1] target + participant : 0.2378459 ±1.11%
## [2] block + participant : 0.02993216 ±0.8%
## [3] target + block + participant : 0.007725106 ±8.73%
## [4] target + block + target:block + participant : 0.0002019399 ±1.28%
## [5] devices + participant : 0.1708543 ±0.74%
## [6] target + devices + participant : 0.04099557 ±1.66%
## [7] block + devices + participant : 0.005261291 ±2.56%
## [8] target + block + devices + participant : 0.001207219 ±1.47%
## [9] target + block + target:block + devices + participant : 3.588998e-05 ±2.02%
## [10] target + devices + target:devices + participant : 0.002809049 ±2.42%
## [11] target + block + devices + target:devices + participant : 8.153603e-05 ±2.33%
## [12] target + block + target:block + devices + target:devices + participant : 2.428224e-06 ±2.33%
## [13] block + devices + block:devices + participant : 0.0003027642 ±1.68%
## [14] target + block + devices + block:devices + participant : 7.233326e-05 ±2%
## [15] target + block + target:block + devices + block:devices + participant : 2.149227e-06 ±2.39%
## [16] target + block + devices + target:devices + block:devices + participant : 5.012381e-06 ±2.81%
## [17] target + block + target:block + devices + target:devices + block:devices + participant : 1.610069e-07 ±5.32%
## [18] target + block + target:block + devices + target:devices + block:devices + target:block:devices + participant : 5.638011e-09 ±4.14%
##
## Against denominator:
## percentcomp ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 0.19 0.086
## block 0.74 0.03 0.011
## block:target 0.32 1.62e-04 3.51e-04
## devices 0.74 0.15 0.062
## devices:target 0.32 1.94e-03 0.004
## block:devices 0.32 2.55e-04 5.54e-04
## block:devices:target 0.05 3.77e-09 6.78e-08
##
## * Compared among: all models
## * Priors odds: uniform-equalWe do not find any effects related to device used. Finally, we run the same 3x3x2 mixed design ANOVA for the washout trials.
RAEDeviceLearningANOVA()## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Angular reach deviations during washout trials across targets, blocks, and devices, trained hand:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 devices 1 61 0.63242864 0.4295495 1.764595e-03
## 3 block 1 61 0.57125565 0.4526692 1.464511e-03
## 5 target 2 122 0.10535655 0.9000854 6.532352e-04
## 4 devices:block 1 61 0.01621664 0.8990865 4.163337e-05
## 6 devices:target 2 122 0.31472898 0.7305776 1.948863e-03
## 7 block:target 2 122 0.17282975 0.8414864 8.334856e-04
## 8 devices:block:target 2 122 0.57698215 0.5631155 2.777131e-03
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 5 target 0.9500933 0.2152722
## 6 devices:target 0.9500933 0.2152722
## 7 block:target 0.9799965 0.5454258
## 8 devices:block:target 0.9799965 0.5454258
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 5 target 0.9524656 0.8914056 0.982364 0.8969583
## 6 devices:target 0.9524656 0.7200054 0.982364 0.7267233
## 7 block:target 0.9803888 0.8373849 1.012617 0.8414864
## 8 devices:block:target 0.9803888 0.5598406 1.012617 0.5631155
## p[HF]<.05
## 5
## 6
## 7
## 8RAEDeviceLearningBayesANOVA()## Bayes factor analysis
## --------------
## [1] target + participant : 0.0293084 ±0.65%
## [2] block + participant : 0.1529623 ±3.16%
## [3] target + block + participant : 0.004487826 ±1.82%
## [4] target + block + target:block + participant : 0.0003911074 ±1.48%
## [5] devices + participant : 0.185308 ±0.83%
## [6] target + devices + participant : 0.005565434 ±1.86%
## [7] block + devices + participant : 0.02881784 ±1.98%
## [8] target + block + devices + participant : 0.0008759945 ±3.65%
## [9] target + block + target:block + devices + participant : 7.086129e-05 ±1.64%
## [10] target + devices + target:devices + participant : 0.0004966013 ±4.84%
## [11] target + block + devices + target:devices + participant : 6.939547e-05 ±1.82%
## [12] target + block + target:block + devices + target:devices + participant : 6.89284e-06 ±5.82%
## [13] block + devices + block:devices + participant : 0.004721889 ±1.86%
## [14] target + block + devices + block:devices + participant : 0.0001527014 ±7.21%
## [15] target + block + target:block + devices + block:devices + participant : 1.502617e-05 ±8.97%
## [16] target + block + devices + target:devices + block:devices + participant : 1.19711e-05 ±3.61%
## [17] target + block + target:block + devices + target:devices + block:devices + participant : 1.055598e-06 ±2.94%
## [18] target + block + target:block + devices + target:devices + block:devices + target:block:devices + participant : 1.867327e-07 ±5.95%
##
## Against denominator:
## angdev ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 0.03 0.011
## block 0.74 0.14 0.056
## block:target 0.32 3.43e-04 7.44e-04
## devices 0.74 0.16 0.068
## devices:target 0.32 4.15e-04 8.99e-04
## block:devices 0.32 3.47e-03 0.008
## block:devices:target 0.05 1.32e-07 2.38e-06
##
## * Compared among: all models
## * Priors odds: uniform-equalWe find no effects related to device used. Taken together, our results suggest that using either a mouse or trackpad to control the cursor does not lead to any differences in learning to compensate for the mirror reversed perturbation.
Completion time
Next, we looked into completion time between the two devices.
plotDeviceCtrlMT()
We conduct the same 3x3x2 (target x block x device) mixed design ANOVA as in learning, but we now have completion time as the dependent variable.
deviceAlignedMTANOVA()## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Movement time during aligned trials across targets, blocks, and devices, trained hand:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 devices 1 61 1.3613313 0.2478479926 0.0182710204
## 3 block 2 122 9.1606857 0.0001965154 * 0.0123585242
## 5 target 2 122 2.4112045 0.0939709859 0.0025917845
## 4 devices:block 2 122 1.2416629 0.2925280532 0.0016931953
## 6 devices:target 2 122 0.5162488 0.5980526507 0.0005560443
## 7 block:target 4 244 0.8528533 0.4929931685 0.0002375235
## 8 devices:block:target 4 244 1.2005976 0.3111549135 0.0003343394
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.3101534 5.588532e-16 *
## 4 devices:block 0.3101534 5.588532e-16 *
## 5 target 0.2883291 6.261160e-17 *
## 6 devices:target 0.2883291 6.261160e-17 *
## 7 block:target 0.6035022 4.401207e-04 *
## 8 devices:block:target 0.6035022 4.401207e-04 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 block 0.5917697 0.002112457 * 0.5966539 0.002052872
## 4 devices:block 0.5917697 0.276975803 0.5966539 0.277310417
## 5 target 0.5842245 0.120418552 0.5886847 0.120132311
## 6 devices:target 0.5842245 0.502333633 0.5886847 0.503667600
## 7 block:target 0.8081101 0.473573200 0.8586623 0.479121721
## 8 devices:block:target 0.8081101 0.311371210 0.8586623 0.311513749
## p[HF]<.05
## 3 *
## 4
## 5
## 6
## 7
## 8## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Movement time during aligned trials across targets, blocks, and devices, untrained hand:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 devices 1 61 0.52280456 0.47241117 0.0059037276
## 3 block 2 122 3.66806859 0.02838158 * 0.0099897617
## 5 target 2 122 1.50936145 0.22514957 0.0012439513
## 4 devices:block 2 122 1.08348472 0.34164786 0.0029717226
## 6 devices:target 2 122 0.48565360 0.61647930 0.0004005930
## 7 block:target 4 244 0.08789517 0.98615829 0.0001281222
## 8 devices:block:target 4 244 0.49388918 0.74023879 0.0007195019
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.4419950 2.304207e-11 *
## 4 devices:block 0.4419950 2.304207e-11 *
## 5 target 0.9834748 6.065923e-01
## 6 devices:target 0.9834748 6.065923e-01
## 7 block:target 0.2681920 3.818763e-13 *
## 8 devices:block:target 0.2681920 3.818763e-13 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 block 0.6418465 0.0487957 * 0.6496464 0.04822887
## 4 devices:block 0.6418465 0.3180755 0.6496464 0.31880306
## 5 target 0.9837434 0.2254235 1.0162551 0.22514957
## 6 devices:target 0.9837434 0.6134069 1.0162551 0.61647930
## 7 block:target 0.5856198 0.9391284 0.6104660 0.94449326
## 8 devices:block:target 0.5856198 0.6408572 0.6104660 0.64859814
## p[HF]<.05
## 3 *
## 4
## 5
## 6
## 7
## 8deviceAlignedMTBayesANOVA()## Bayes factor analysis
## --------------
## [1] target + participant : 3.160177 ±0.95%
## [2] block + participant : 2051501898 ±0.6%
## [3] target + block + participant : 11770719133 ±2.41%
## [4] target + block + target:block + participant : 98305554 ±2.03%
## [5] devices + participant : 0.6661951 ±1.02%
## [6] target + devices + participant : 2.199002 ±2.11%
## [7] block + devices + participant : 1489744087 ±3.84%
## [8] target + block + devices + participant : 8701766053 ±6.72%
## [9] target + block + target:block + devices + participant : 66391670 ±2.31%
## [10] target + devices + target:devices + participant : 0.1918966 ±2.37%
## [11] target + block + devices + target:devices + participant : 781908950 ±3.2%
## [12] target + block + target:block + devices + target:devices + participant : 6413225 ±2.7%
## [13] block + devices + block:devices + participant : 693401001 ±3.21%
## [14] target + block + devices + block:devices + participant : 4976865731 ±21.37%
## [15] target + block + target:block + devices + block:devices + participant : 32984918 ±2.32%
## [16] target + block + devices + target:devices + block:devices + participant : 415018125 ±10.53%
## [17] target + block + target:block + devices + target:devices + block:devices + participant : 3120392 ±2.74%
## [18] target + block + target:block + devices + target:devices + block:devices + target:block:devices + participant : 109196.3 ±3.62%
##
## Against denominator:
## movementtime ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 0.86 2.26
## block 0.74 1.00 1.54e+09
## block:target 0.32 6.67e-03 0.015
## devices 0.74 0.55 0.440
## devices:target 0.32 0.04 0.087
## block:devices 0.32 0.20 0.531
## block:devices:target 0.05 3.51e-06 6.32e-05
##
## * Compared among: all models
## * Priors odds: uniform-equalBayes factor analysis
## --------------
## [1] target + participant : 0.09204222 ±13.24%
## [2] block + participant : 7327.128 ±1.23%
## [3] target + block + participant : 667.4959 ±5.14%
## [4] target + block + target:block + participant : 5.937868 ±1.66%
## [5] devices + participant : 0.4284358 ±0.82%
## [6] target + devices + participant : 0.03418 ±1.82%
## [7] block + devices + participant : 3255.812 ±1.8%
## [8] target + block + devices + participant : 262.8512 ±1.76%
## [9] target + block + target:block + devices + participant : 2.54522 ±2.07%
## [10] target + devices + target:devices + participant : 0.001956269 ±1.81%
## [11] target + block + devices + target:devices + participant : 15.66977 ±1.8%
## [12] target + block + target:block + devices + target:devices + participant : 0.1529046 ±4.21%
## [13] block + devices + block:devices + participant : 1407.314 ±2.17%
## [14] target + block + devices + block:devices + participant : 115.8729 ±2.79%
## [15] target + block + target:block + devices + block:devices + participant : 1.10539 ±2.27%
## [16] target + block + devices + target:devices + block:devices + participant : 6.883529 ±2.65%
## [17] target + block + target:block + devices + target:devices + block:devices + participant : 0.0664645 ±2.45%
## [18] target + block + target:block + devices + target:devices + block:devices + target:block:devices + participant : 0.002860552 ±5.03%
##
## Against denominator:
## movementtime ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 0.08 0.032
## block 0.74 1.00 3.00e+03
## block:target 0.32 7.51e-04 0.002
## devices 0.74 0.39 0.226
## devices:target 0.32 1.74e-03 0.004
## block:devices 0.32 0.12 0.288
## block:devices:target 0.05 2.19e-07 3.94e-06
##
## * Compared among: all models
## * Priors odds: uniform-equalWe find no device-related effects. We repeat the test for the mirror reversed trials.
deviceMirrorMTANOVA()## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 devices 1 61 2.36353429 1.293718e-01 1.084670e-02
## 3 target 2 122 19.82819934 3.497702e-08 * 5.922950e-02
## 5 block 2 122 31.44561522 9.683996e-12 * 1.037904e-01
## 4 devices:target 2 122 0.00642518 9.935958e-01 2.040081e-05
## 6 devices:block 2 122 1.43145493 2.429456e-01 5.244229e-03
## 7 target:block 4 244 3.43595657 9.374931e-03 * 1.654364e-02
## 8 devices:target:block 4 244 0.11076984 9.786752e-01 5.420190e-04
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 target 0.9744371 4.598487e-01
## 4 devices:target 0.9744371 4.598487e-01
## 5 block 0.6681273 5.568999e-06 *
## 6 devices:block 0.6681273 5.568999e-06 *
## 7 target:block 0.2711276 5.126848e-13 *
## 8 devices:target:block 0.2711276 5.126848e-13 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 target 0.9750743 4.937779e-08 * 1.0068545 3.497702e-08
## 4 devices:target 0.9750743 9.928407e-01 1.0068545 9.935958e-01
## 5 block 0.7508225 2.189013e-09 * 0.7655841 1.586700e-09
## 6 devices:block 0.7508225 2.431447e-01 0.7655841 2.432691e-01
## 7 target:block 0.5713525 2.917151e-02 * 0.5948071 2.739186e-02
## 8 devices:target:block 0.5713525 9.175299e-01 0.5948071 9.236751e-01
## p[HF]<.05
## 3 *
## 4
## 5 *
## 6
## 7 *
## 8deviceMirrorMTBayesANOVA()## Bayes factor analysis
## --------------
## [1] target + participant : 7677218 ±0.91%
## [2] block + participant : 5.012626e+16 ±0.71%
## [3] target + block + participant : 1.736713e+25 ±2.17%
## [4] target + block + target:block + participant : 2.261787e+25 ±2%
## [5] devices + participant : 0.433624 ±1.25%
## [6] target + devices + participant : 3989239 ±9.49%
## [7] block + devices + participant : 2.363685e+16 ±1.91%
## [8] target + block + devices + participant : 8.381492e+24 ±1.81%
## [9] target + block + target:block + devices + participant : 1.079219e+25 ±1.98%
## [10] target + devices + target:devices + participant : 151896.2 ±1.86%
## [11] target + block + devices + target:devices + participant : 3.854058e+23 ±3.1%
## [12] target + block + target:block + devices + target:devices + participant : 4.915302e+23 ±2.65%
## [13] block + devices + block:devices + participant : 4.989314e+15 ±2.59%
## [14] target + block + devices + block:devices + participant : 2.102412e+24 ±3.6%
## [15] target + block + target:block + devices + block:devices + participant : 2.708688e+24 ±2.63%
## [16] target + block + devices + target:devices + block:devices + participant : 9.106789e+22 ±3.62%
## [17] target + block + target:block + devices + target:devices + block:devices + participant : 1.282142e+23 ±5.41%
## [18] target + block + target:block + devices + target:devices + block:devices + target:block:devices + participant : 3.464764e+21 ±3.7%
##
## Against denominator:
## movementtime ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 1.00 2.95e+08
## block 0.74 1.00 1.97e+18
## block:target 0.32 0.56 2.81
## devices 0.74 0.39 0.224
## devices:target 0.32 0.02 0.037
## block:devices 0.32 0.08 0.182
## block:devices:target 0.05 5.32e-05 9.58e-04
##
## * Compared among: all models
## * Priors odds: uniform-equalWe find no device-related effects. Finally, we conduct the test for washout trials.
deviceRAEMTANOVA()## Warning: You have removed one or more levels from variable "block". Refactoring
## for ANOVA.## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Movement time during washout trials across targets, blocks, and devices, trained hand:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 devices 1 61 2.1349369 1.491086e-01 0.0263468832
## 3 block 1 61 33.1891541 2.935277e-07 * 0.0158326605
## 5 target 2 122 4.6816600 1.099078e-02 * 0.0078773785
## 4 devices:block 1 61 4.7946598 3.238280e-02 * 0.0023186672
## 6 devices:target 2 122 0.9814930 3.776904e-01 0.0016618101
## 7 block:target 2 122 0.1618102 8.507848e-01 0.0002488015
## 8 devices:block:target 2 122 0.4615610 6.313951e-01 0.0007093751
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 5 target 0.9984388 0.9542090
## 6 devices:target 0.9984388 0.9542090
## 7 block:target 0.9391364 0.1520056
## 8 devices:block:target 0.9391364 0.1520056
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 5 target 0.9984412 0.01102987 * 1.0322057 0.01099078
## 6 devices:target 0.9984412 0.37758658 1.0322057 0.37769036
## 7 block:target 0.9426282 0.83861482 0.9717195 0.84492612
## 8 devices:block:target 0.9426282 0.62000645 0.9717195 0.62586396
## p[HF]<.05
## 5 *
## 6
## 7
## 8deviceRAEMTBayesANOVA()## Bayes factor analysis
## --------------
## [1] target + participant : 1.55045 ±0.61%
## [2] block + participant : 570530 ±11.73%
## [3] target + block + participant : 1169372 ±1.29%
## [4] target + block + target:block + participant : 71341.76 ±3.66%
## [5] devices + participant : 0.8194107 ±2.11%
## [6] target + devices + participant : 1.23075 ±1.47%
## [7] block + devices + participant : 424539.1 ±2.98%
## [8] target + block + devices + participant : 1064970 ±5.05%
## [9] target + block + target:block + devices + participant : 56932.91 ±2.63%
## [10] target + devices + target:devices + participant : 0.1848855 ±3.02%
## [11] target + block + devices + target:devices + participant : 143930.8 ±2.67%
## [12] target + block + target:block + devices + target:devices + participant : 9023.148 ±3.32%
## [13] block + devices + block:devices + participant : 331892.9 ±3.52%
## [14] target + block + devices + block:devices + participant : 794406.2 ±3.82%
## [15] target + block + target:block + devices + block:devices + participant : 49193.87 ±5.95%
## [16] target + block + devices + target:devices + block:devices + participant : 118843.1 ±3.79%
## [17] target + block + target:block + devices + target:devices + block:devices + participant : 8410.172 ±11.32%
## [18] target + block + target:block + devices + target:devices + block:devices + target:block:devices + participant : 1068.044 ±3.56%
##
## Against denominator:
## movementtime ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 0.72 0.939
## block 0.74 1.00 3.59e+05
## block:target 0.32 0.04 0.092
## devices 0.74 0.62 0.592
## devices:target 0.32 0.06 0.134
## block:devices 0.32 0.27 0.805
## block:devices:target 0.05 2.22e-04 0.004
##
## * Compared among: all models
## * Priors odds: uniform-equalWe find a device x block interaction in the frequentist test, which did not hold up in the Bayesian test. Overall, completion time did not differ between mouse and trackpad users.
Path length
We also looked into path lengths for the two devices.
plotDeviceCtrlPL()
We then repeat the same set of ANOVAs as in the section above, but use path length as the dependent variable. We first look into the aligned trials.
deviceAlignedPLANOVA()## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Path length during aligned trials across targets, blocks, and devices, trained hand:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 devices 1 61 0.5504171 0.4609944122 0.0046867046
## 3 block 2 122 1.8857279 0.1561141707 0.0046772311
## 5 target 2 122 7.7126879 0.0007012401 * 0.0165534340
## 4 devices:block 2 122 2.4134929 0.0937643504 0.0059784376
## 6 devices:target 2 122 0.2493412 0.7797101483 0.0005438629
## 7 block:target 4 244 0.2184723 0.9279933240 0.0006908018
## 8 devices:block:target 4 244 0.9668977 0.4262749757 0.0030500783
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.8091827 0.001743401 *
## 4 devices:block 0.8091827 0.001743401 *
## 5 target 0.9719612 0.426057099
## 6 devices:target 0.9719612 0.426057099
## 7 block:target 0.7121979 0.016956811 *
## 8 devices:block:target 0.7121979 0.016956811 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 block 0.8397594 0.1633126096 0.8608339 0.1623910536
## 4 devices:block 0.8397594 0.1036110593 0.8608339 0.1022764312
## 5 target 0.9727259 0.0007958683 * 1.0043089 0.0007012401
## 6 devices:target 0.9727259 0.7736631185 1.0043089 0.7797101483
## 7 block:target 0.8653131 0.9070130252 0.9237151 0.9168466151
## 8 devices:block:target 0.8653131 0.4180711098 0.9237151 0.4218219495
## p[HF]<.05
## 3
## 4
## 5 *
## 6
## 7
## 8## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Path length during aligned trials across targets, blocks, and devices, untrained hand:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 devices 1 61 8.840270 0.0042146884 * 0.041076047
## 3 block 2 122 8.196806 0.0004569524 * 0.021254677
## 5 target 2 122 3.189158 0.0446640054 * 0.009075748
## 4 devices:block 2 122 3.492965 0.0334862964 * 0.009169250
## 6 devices:target 2 122 5.422812 0.0055432854 * 0.015334835
## 7 block:target 4 244 1.830192 0.1236138273 0.010909692
## 8 devices:block:target 4 244 2.947909 0.0209193088 * 0.017456054
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.9176398 0.075886975
## 4 devices:block 0.9176398 0.075886975
## 5 target 0.8828178 0.023775616 *
## 6 devices:target 0.8828178 0.023775616 *
## 7 block:target 0.6347790 0.001403033 *
## 8 devices:block:target 0.6347790 0.001403033 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 block 0.9239068 0.0006698352 * 0.9514817 0.0005830777
## 4 devices:block 0.9239068 0.0372164464 * 0.9514817 0.0358188578
## 5 target 0.8951091 0.0504807632 0.9204014 0.0490134867
## 6 devices:target 0.8951091 0.0074769310 * 0.9204014 0.0069557507
## 7 block:target 0.8090715 0.1383563219 0.8597513 0.1342915754
## 8 devices:block:target 0.8090715 0.0304052879 * 0.8597513 0.0275191056
## p[HF]<.05
## 3 *
## 4 *
## 5 *
## 6 *
## 7
## 8 *deviceAlignedPLBayesANOVA()## Bayes factor analysis
## --------------
## [1] target + participant : 202.2616 ±0.64%
## [2] block + participant : 0.04522572 ±0.82%
## [3] target + block + participant : 9.682648 ±1.63%
## [4] target + block + target:block + participant : 0.07791055 ±3.32%
## [5] devices + participant : 0.3382046 ±0.89%
## [6] target + devices + participant : 71.83299 ±2.81%
## [7] block + devices + participant : 0.0154565 ±1.29%
## [8] target + block + devices + participant : 3.315836 ±1.77%
## [9] target + block + target:block + devices + participant : 0.02504114 ±2.08%
## [10] target + devices + target:devices + participant : 3.801927 ±1.9%
## [11] target + block + devices + target:devices + participant : 0.1780805 ±1.48%
## [12] target + block + target:block + devices + target:devices + participant : 0.001372694 ±1.69%
## [13] block + devices + block:devices + participant : 0.00903809 ±1.54%
## [14] target + block + devices + block:devices + participant : 2.17292 ±3.3%
## [15] target + block + target:block + devices + block:devices + participant : 0.01701366 ±4.91%
## [16] target + block + devices + target:devices + block:devices + participant : 0.1168295 ±2.23%
## [17] target + block + target:block + devices + target:devices + block:devices + participant : 0.001025569 ±5.21%
## [18] target + block + target:block + devices + target:devices + block:devices + target:block:devices + participant : 6.861902e-05 ±3.67%
##
## Against denominator:
## pathlength ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 1.00 74.45
## block 0.74 0.05 0.020
## block:target 0.32 4.15e-04 9.00e-04
## devices 0.74 0.28 0.137
## devices:target 0.32 0.01 0.031
## block:devices 0.32 7.86e-03 0.017
## block:devices:target 0.05 2.33e-07 4.19e-06
##
## * Compared among: all models
## * Priors odds: uniform-equalBayes factor analysis
## --------------
## [1] target + participant : 0.04487032 ±3.05%
## [2] block + participant : 2.601413 ±0.62%
## [3] target + block + participant : 0.1170326 ±1.8%
## [4] target + block + target:block + participant : 0.01082565 ±66.18%
## [5] devices + participant : 6.954562 ±1.49%
## [6] target + devices + participant : 0.3160146 ±5.86%
## [7] block + devices + participant : 18.68958 ±2.12%
## [8] target + block + devices + participant : 0.796574 ±1.4%
## [9] target + block + target:block + devices + participant : 0.02632614 ±2.56%
## [10] target + devices + target:devices + participant : 1.284815 ±2.06%
## [11] target + block + devices + target:devices + participant : 3.731052 ±3.29%
## [12] target + block + target:block + devices + target:devices + participant : 0.122593 ±3.69%
## [13] block + devices + block:devices + participant : 11.41553 ±1.53%
## [14] target + block + devices + block:devices + participant : 0.5132467 ±2.62%
## [15] target + block + target:block + devices + block:devices + participant : 0.01558105 ±1.79%
## [16] target + block + devices + target:devices + block:devices + participant : 2.35803 ±3.99%
## [17] target + block + target:block + devices + target:devices + block:devices + participant : 0.07702707 ±2.36%
## [18] target + block + target:block + devices + target:devices + block:devices + target:block:devices + participant : 0.1471723 ±3.7%
##
## Against denominator:
## pathlength ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 0.19 0.084
## block 0.74 0.81 1.51
## block:target 0.32 7.96e-03 0.017
## devices 0.74 0.92 4.40
## devices:target 0.32 0.15 0.394
## block:devices 0.32 0.29 0.882
## block:devices:target 0.05 2.93e-03 0.053
##
## * Compared among: all models
## * Priors odds: uniform-equalWe find no device-related effects for the dominant hand, but find a main effect of device and a target x block x device interaction for the nondominant hand. We conduct follow-up tests on the main effect of device, regardless of target or block.
deviceAlignedPLComparisons()##
## Welch Two Sample t-test
##
## data: mousedat$pathlength and trackdat$pathlength
## t = 2.7565, df = 29.151, p-value = 0.009974
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## 0.01569437 0.10587877
## sample estimates:
## mean of x mean of y
## 0.5491369 0.4883503
##
## Bayesian t-test (mouse vs. trackpad):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 9.43347 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZSWe find longer path lengths for mouse users, than trackpad users.
Next, we test for effects in the mirror reversed trials.
deviceMirrorPLANOVA()## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 devices 1 61 0.1568998 6.934091e-01 0.0004802307
## 3 target 2 122 19.8162205 3.529468e-08 * 0.0615998597
## 5 block 2 122 23.6154692 2.141333e-09 * 0.0993070369
## 4 devices:target 2 122 0.8487445 4.304629e-01 0.0028036802
## 6 devices:block 2 122 0.2824242 7.544454e-01 0.0013168500
## 7 target:block 4 244 4.1297597 2.954244e-03 * 0.0216158047
## 8 devices:target:block 4 244 1.0035359 4.063112e-01 0.0053400430
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 target 0.9996237 9.887710e-01
## 4 devices:target 0.9996237 9.887710e-01
## 5 block 0.4608833 8.085902e-11 *
## 6 devices:block 0.4608833 8.085902e-11 *
## 7 target:block 0.1833458 1.151926e-17 *
## 8 devices:target:block 0.1833458 1.151926e-17 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 target 0.9996238 3.547868e-08 * 1.033490 3.529468e-08
## 4 devices:target 0.9996238 4.304265e-01 1.033490 4.304629e-01
## 5 block 0.6497233 7.077443e-07 * 0.657998 6.167683e-07
## 6 devices:block 0.6497233 6.573445e-01 0.657998 6.602508e-01
## 7 target:block 0.6474644 1.065412e-02 * 0.678697 9.497773e-03
## 8 devices:target:block 0.6474644 3.846891e-01 0.678697 3.872558e-01
## p[HF]<.05
## 3 *
## 4
## 5 *
## 6
## 7 *
## 8deviceMirrorPLBayesANOVA()## Bayes factor analysis
## --------------
## [1] target + participant : 1615615 ±0.73%
## [2] block + participant : 6.890333e+13 ±1.15%
## [3] target + block + participant : 1.741823e+21 ±1.76%
## [4] target + block + target:block + participant : 8.416184e+21 ±1.06%
## [5] devices + participant : 0.1490384 ±1.08%
## [6] target + devices + participant : 249079.4 ±1.44%
## [7] block + devices + participant : 1.039465e+13 ±1.45%
## [8] target + block + devices + participant : 2.712909e+20 ±1.59%
## [9] target + block + target:block + devices + participant : 1.307539e+21 ±1.81%
## [10] target + devices + target:devices + participant : 21068.22 ±6.57%
## [11] target + block + devices + target:devices + participant : 3.41636e+19 ±22.74%
## [12] target + block + target:block + devices + target:devices + participant : 1.2457e+20 ±1.82%
## [13] block + devices + block:devices + participant : 795675641274 ±16.27%
## [14] target + block + devices + block:devices + participant : 1.813866e+19 ±2.03%
## [15] target + block + target:block + devices + block:devices + participant : 9.068139e+19 ±2.56%
## [16] target + block + devices + target:devices + block:devices + participant : 1.752676e+18 ±4.17%
## [17] target + block + target:block + devices + target:devices + block:devices + participant : 1.032851e+19 ±11.08%
## [18] target + block + target:block + devices + target:devices + block:devices + target:block:devices + participant : 7.032594e+17 ±2.5%
##
## Against denominator:
## pathlength ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 1.00 5.36e+07
## block 0.74 1.00 2.28e+15
## block:target 0.32 0.83 10.43
## devices 0.74 0.15 0.065
## devices:target 0.32 0.01 0.031
## block:devices 0.32 0.01 0.022
## block:devices:target 0.05 5.85e-05 0.001
##
## * Compared among: all models
## * Priors odds: uniform-equalWe find no device-related effects. We then test for an effect during washout trials.
deviceRAEPLANOVA()## Warning: You have removed one or more levels from variable "block". Refactoring
## for ANOVA.## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Path length during washout trials across targets, blocks, and devices, trained hand:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 devices 1 61 0.48478101 0.4889093 0.0029353455
## 3 block 1 61 6.02978819 0.0169312 * 0.0143750276
## 5 target 2 122 0.02424711 0.9760492 0.0001111229
## 4 devices:block 1 61 0.06538257 0.7990426 0.0001581205
## 6 devices:target 2 122 2.02521820 0.1363779 0.0091970993
## 7 block:target 2 122 0.94176174 0.3927563 0.0031154151
## 8 devices:block:target 2 122 1.21519218 0.3002180 0.0040163096
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 5 target 0.9204901 0.08328636
## 6 devices:target 0.9204901 0.08328636
## 7 block:target 0.9640826 0.33375424
## 8 devices:block:target 0.9640826 0.33375424
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 5 target 0.9263463 0.9697595 0.9541173 0.9723113
## 6 devices:target 0.9263463 0.1401996 0.9541173 0.1387575
## 7 block:target 0.9653279 0.3900901 0.9962922 0.3924769
## 8 devices:block:target 0.9653279 0.2994055 0.9962922 0.3001350
## p[HF]<.05
## 5
## 6
## 7
## 8deviceRAEPLBayesANOVA()## Bayes factor analysis
## --------------
## [1] target + participant : 0.0388417 ±2.56%
## [2] block + participant : 8.76326 ±1.26%
## [3] target + block + participant : 0.342099 ±2%
## [4] target + block + target:block + participant : 0.03695292 ±2.35%
## [5] devices + participant : 0.2454588 ±0.86%
## [6] target + devices + participant : 0.00962651 ±1.52%
## [7] block + devices + participant : 2.257699 ±2.33%
## [8] target + block + devices + participant : 0.08856806 ±3.11%
## [9] target + block + target:block + devices + participant : 0.009694597 ±2.72%
## [10] target + devices + target:devices + participant : 0.004071873 ±2.22%
## [11] target + block + devices + target:devices + participant : 0.03908659 ±2.54%
## [12] target + block + target:block + devices + target:devices + participant : 0.005823351 ±26.34%
## [13] block + devices + block:devices + participant : 0.394138 ±3.04%
## [14] target + block + devices + block:devices + participant : 0.01496639 ±1.88%
## [15] target + block + target:block + devices + block:devices + participant : 0.001856708 ±6.35%
## [16] target + block + devices + target:devices + block:devices + participant : 0.0075188 ±9.74%
## [17] target + block + target:block + devices + target:devices + block:devices + participant : 0.0007559071 ±3.88%
## [18] target + block + target:block + devices + target:devices + block:devices + target:block:devices + participant : 0.0001675924 ±3.65%
##
## Against denominator:
## pathlength ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 0.05 0.017
## block 0.74 0.90 3.29
## block:target 0.32 4.17e-03 0.009
## devices 0.74 0.23 0.108
## devices:target 0.32 4.33e-03 0.009
## block:devices 0.32 0.03 0.071
## block:devices:target 0.05 1.26e-05 2.27e-04
##
## * Compared among: all models
## * Priors odds: uniform-equalWe find no device-related effects. Overall, we only found path length differences between mouse and trackpad users in the aligned trials using the nondominant hand. This difference could be due to participants not being used to controlling the mouse with their nondominant hand, while it is easier to use the trackpad with both hands.
Sex differences: Males vs. females
We repeat the same set of analyses but now split the data according to males (N =18) and females (N = 44). Note that one participant did not identify as either male or female, so they are not included in the comparisons below.
Learning
plotSexCtrl()
The disproportionately smaller sample for males contribute to the variability we observe in their data. We first conduct a 3x3x2 (trackpad x block x sex) mixed design ANOVA, with trackpad and block as within-subjects factors and sex as a between-subjects factor, for the aligned trials for both hands.
sexAlignedLearningANOVA()## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Angular reach deviations during aligned trials across targets, blocks, and sexes, trained hand:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 sex 1 60 0.5394135 0.46553660 0.0009574108
## 3 block 2 120 0.5183481 0.59683066 0.0019129375
## 5 target 2 120 2.4567170 0.09001728 0.0091469468
## 4 sex:block 2 120 1.0032605 0.36973637 0.0036958682
## 6 sex:target 2 120 1.9289069 0.14978564 0.0071959242
## 7 block:target 4 240 1.3599332 0.24854016 0.0100097880
## 8 sex:block:target 4 240 0.1425064 0.96615417 0.0010584024
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.9926280 0.8038997
## 4 sex:block 0.9926280 0.8038997
## 5 target 0.9461635 0.1954351
## 6 sex:target 0.9461635 0.1954351
## 7 block:target 0.8542897 0.4192406
## 8 sex:block:target 0.8542897 0.4192406
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 block 0.9926819 0.59550997 1.0265271 0.59683066
## 4 sex:block 0.9926819 0.36928123 1.0265271 0.36973637
## 5 target 0.9489138 0.09309127 0.9790295 0.09126875
## 6 sex:target 0.9489138 0.15222886 0.9790295 0.15079004
## 7 block:target 0.9292033 0.25100875 0.9981915 0.24860439
## 8 sex:block:target 0.9292033 0.95929125 0.9981915 0.96599501
## p[HF]<.05
## 3
## 4
## 5
## 6
## 7
## 8## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Angular reach deviations during aligned trials across targets, blocks, and sexes, untrained hand:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 sex 1 60 0.002146009 0.9632050 5.415639e-06
## 3 block 2 120 1.223717409 0.2977785 3.739521e-03
## 5 target 2 120 1.201195459 0.3044253 4.949721e-03
## 4 sex:block 2 120 0.195685723 0.8225325 5.998746e-04
## 6 sex:target 2 120 0.633054229 0.5327314 2.614724e-03
## 7 block:target 4 240 0.765081984 0.5488941 5.277512e-03
## 8 sex:block:target 4 240 0.116448704 0.9766073 8.068697e-04
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.9105883 0.0630958644
## 4 sex:block 0.9105883 0.0630958644
## 5 target 0.9974434 0.9272656248
## 6 sex:target 0.9974434 0.9272656248
## 7 block:target 0.5755546 0.0001799418 *
## 8 sex:block:target 0.5755546 0.0001799418 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF] p[HF]<.05
## 3 block 0.9179266 0.2958307 0.9454884 0.2965403
## 4 sex:block 0.9179266 0.8040813 0.9454884 0.8105293
## 5 target 0.9974500 0.3043624 1.0317101 0.3044253
## 6 sex:target 0.9974500 0.5323457 1.0317101 0.5327314
## 7 block:target 0.8087236 0.5238486 0.8602493 0.5311098
## 8 sex:block:target 0.8087236 0.9585291 0.8602493 0.9645176sexAlignedLearningBayesANOVA()## Bayes factor analysis
## --------------
## [1] target + participant : 1.756189 ±0.8%
## [2] block + participant : 0.0221445 ±0.55%
## [3] target + block + participant : 0.03843303 ±0.91%
## [4] target + block + target:block + participant : 0.006600016 ±1.02%
## [5] sex + participant : 0.1525161 ±1.01%
## [6] target + sex + participant : 0.2664563 ±1.67%
## [7] block + sex + participant : 0.003509059 ±3.21%
## [8] target + block + sex + participant : 0.006136525 ±2.28%
## [9] target + block + target:block + sex + participant : 0.001020887 ±1.39%
## [10] target + sex + target:sex + participant : 0.0854652 ±7.25%
## [11] target + block + sex + target:sex + participant : 0.001938083 ±5.49%
## [12] target + block + target:block + sex + target:sex + participant : 0.0003283374 ±2.45%
## [13] block + sex + block:sex + participant : 0.0003800021 ±1.88%
## [14] target + block + sex + block:sex + participant : 0.0007962365 ±9.53%
## [15] target + block + target:block + sex + block:sex + participant : 0.0001233945 ±3.52%
## [16] target + block + sex + target:sex + block:sex + participant : 0.0002034265 ±2.62%
## [17] target + block + target:block + sex + target:sex + block:sex + participant : 3.592424e-05 ±2.42%
## [18] target + block + target:block + sex + target:sex + block:sex + target:block:sex + participant : 1.288333e-06 ±2.45%
##
## Against denominator:
## angdev ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 0.65 0.656
## block 0.74 0.02 0.009
## block:target 0.32 2.43e-03 0.005
## sex 0.74 0.16 0.066
## sex:target 0.32 0.03 0.059
## block:sex 0.32 4.61e-04 9.99e-04
## block:sex:target 0.05 3.85e-07 6.94e-06
##
## * Compared among: all models
## * Priors odds: uniform-equalBayes factor analysis
## --------------
## [1] target + participant : 0.04505332 ±0.71%
## [2] block + participant : 0.07768367 ±1.39%
## [3] target + block + participant : 0.004318006 ±18.6%
## [4] target + block + target:block + participant : 0.0001048608 ±6.38%
## [5] sex + participant : 0.144439 ±1.38%
## [6] target + sex + participant : 0.006423561 ±1.39%
## [7] block + sex + participant : 0.01117543 ±2.18%
## [8] target + block + sex + participant : 0.0004845439 ±1.59%
## [9] target + block + target:block + sex + participant : 1.389294e-05 ±1.73%
## [10] target + sex + target:sex + participant : 0.0005599768 ±2.15%
## [11] target + block + sex + target:sex + participant : 4.316519e-05 ±2.3%
## [12] target + block + target:block + sex + target:sex + participant : 1.314015e-06 ±5.78%
## [13] block + sex + block:sex + participant : 0.0006067108 ±3.17%
## [14] target + block + sex + block:sex + participant : 2.608596e-05 ±2.09%
## [15] target + block + target:block + sex + block:sex + participant : 7.923319e-07 ±8.8%
## [16] target + block + sex + target:sex + block:sex + participant : 2.275596e-06 ±2.34%
## [17] target + block + target:block + sex + target:sex + block:sex + participant : 6.527566e-08 ±3.75%
## [18] target + block + target:block + sex + target:sex + block:sex + target:block:sex + participant : 2.000254e-09 ±5.52%
##
## Against denominator:
## angdev ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 0.04 0.017
## block 0.74 0.07 0.028
## block:target 0.32 9.37e-05 2.03e-04
## sex 0.74 0.13 0.052
## sex:target 0.32 4.70e-04 0.001
## block:sex 0.32 4.93e-04 0.001
## block:sex:target 0.05 1.55e-09 2.79e-08
##
## * Compared among: all models
## * Priors odds: uniform-equalWe do not find any sex-related effects. Next, we conduct the same test for mirror reversed reaches.
sexmirrorANOVA()## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 sex 1 60 0.8275751 0.36661468 0.0013625906
## 3 target 2 120 2.9845908 0.05432707 0.0091593619
## 5 block 2 120 0.3289519 0.72032453 0.0012868471
## 4 sex:target 2 120 0.2645141 0.76802520 0.0008185963
## 6 sex:block 2 120 0.8985704 0.40987284 0.0035073572
## 7 target:block 4 240 0.8061139 0.52230378 0.0064105181
## 8 sex:target:block 4 240 1.1562535 0.33085051 0.0091694264
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 target 0.076435424 1.140757e-33 *
## 4 sex:target 0.076435424 1.140757e-33 *
## 5 block 0.793782277 1.099490e-03 *
## 6 sex:block 0.793782277 1.099490e-03 *
## 7 target:block 0.001309785 1.054189e-77 *
## 8 sex:target:block 0.001309785 1.054189e-77 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 target 0.5198682 0.08759622 0.5208925 0.08751342
## 4 sex:target 0.5198682 0.61804793 0.5208925 0.61850889
## 5 block 0.8290377 0.67961611 0.8496686 0.68499075
## 6 sex:block 0.8290377 0.39365414 0.8496686 0.39581388
## 7 target:block 0.4234870 0.43111343 0.4344782 0.43388555
## 8 sex:target:block 0.4234870 0.31223629 0.4344782 0.31321850
## p[HF]<.05
## 3
## 4
## 5
## 6
## 7
## 8sexmirrorBayesANOVA()## Bayes factor analysis
## --------------
## [1] target + participant : 0.2109656 ±0.61%
## [2] block + participant : 0.02977687 ±1.98%
## [3] target + block + participant : 0.006213569 ±1.16%
## [4] target + block + target:block + participant : 0.0001676786 ±1.14%
## [5] sex + participant : 0.1624103 ±0.94%
## [6] target + sex + participant : 0.03458112 ±1.44%
## [7] block + sex + participant : 0.004836822 ±2.8%
## [8] target + block + sex + participant : 0.001065342 ±3.76%
## [9] target + block + target:block + sex + participant : 2.722685e-05 ±1.59%
## [10] target + sex + target:sex + participant : 0.001813893 ±1.44%
## [11] target + block + sex + target:sex + participant : 5.464334e-05 ±2.87%
## [12] target + block + target:block + sex + target:sex + participant : 1.472274e-06 ±2.2%
## [13] block + sex + block:sex + participant : 0.0005231149 ±4.5%
## [14] target + block + sex + block:sex + participant : 0.0001081838 ±1.66%
## [15] target + block + target:block + sex + block:sex + participant : 3.42051e-06 ±8.3%
## [16] target + block + sex + target:sex + block:sex + participant : 5.680804e-06 ±2.35%
## [17] target + block + target:block + sex + target:sex + block:sex + participant : 1.687915e-07 ±3.06%
## [18] target + block + target:block + sex + target:sex + block:sex + target:block:sex + participant : 2.572285e-08 ±2.64%
##
## Against denominator:
## percentcomp ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 0.18 0.076
## block 0.74 0.03 0.011
## block:target 0.32 1.38e-04 2.98e-04
## sex 0.74 0.14 0.059
## sex:target 0.32 1.29e-03 0.003
## block:sex 0.32 4.41e-04 9.56e-04
## block:sex:target 0.05 1.77e-08 3.19e-07
##
## * Compared among: all models
## * Priors odds: uniform-equalThere are no sex-related effects. Finally, we test washout trials.
RAESexLearningANOVA()## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Angular reach deviations during washout trials across targets, blocks, and sexes, trained hand:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 sex 1 60 0.54789267 0.4620667 0.0015796592
## 3 block 1 60 1.71433698 0.1954156 0.0043990971
## 5 target 2 120 0.03515675 0.9654640 0.0002175041
## 4 sex:block 1 60 1.27958189 0.2624780 0.0032871553
## 6 sex:target 2 120 0.14082482 0.8687848 0.0008706709
## 7 block:target 2 120 0.32302586 0.7245827 0.0016168744
## 8 sex:block:target 2 120 0.31673716 0.7291294 0.0015854469
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 5 target 0.9268801 0.1064622
## 6 sex:target 0.9268801 0.1064622
## 7 block:target 0.9820799 0.5865858
## 8 sex:block:target 0.9820799 0.5865858
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF] p[HF]<.05
## 5 target 0.9318623 0.9582006 0.9605638 0.9614379
## 6 sex:target 0.9318623 0.8547447 0.9605638 0.8608600
## 7 block:target 0.9823954 0.7207491 1.0153512 0.7245827
## 8 sex:block:target 0.9823954 0.7252856 1.0153512 0.7291294RAESexLearningBayesANOVA()## Bayes factor analysis
## --------------
## [1] target + participant : 0.02970251 ±1.01%
## [2] block + participant : 0.174089 ±1.56%
## [3] target + block + participant : 0.005091281 ±2.6%
## [4] target + block + target:block + participant : 0.0004791891 ±4.13%
## [5] sex + participant : 0.187881 ±0.9%
## [6] target + sex + participant : 0.005913391 ±4.04%
## [7] block + sex + participant : 0.03392841 ±3.61%
## [8] target + block + sex + participant : 0.0009778514 ±2.91%
## [9] target + block + target:block + sex + participant : 8.957044e-05 ±3.67%
## [10] target + sex + target:sex + participant : 0.0004200416 ±3.55%
## [11] target + block + sex + target:sex + participant : 9.027286e-05 ±19.96%
## [12] target + block + target:block + sex + target:sex + participant : 6.992947e-06 ±4.71%
## [13] block + sex + block:sex + participant : 0.009902068 ±5.09%
## [14] target + block + sex + block:sex + participant : 0.0002883972 ±3.05%
## [15] target + block + target:block + sex + block:sex + participant : 2.679538e-05 ±3.05%
## [16] target + block + sex + target:sex + block:sex + participant : 2.182435e-05 ±3.86%
## [17] target + block + target:block + sex + target:sex + block:sex + participant : 2.094525e-06 ±4.02%
## [18] target + block + target:block + sex + target:sex + block:sex + target:block:sex + participant : 2.982082e-07 ±4.3%
##
## Against denominator:
## angdev ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 0.03 0.011
## block 0.74 0.16 0.066
## block:target 0.32 4.18e-04 9.05e-04
## sex 0.74 0.17 0.071
## sex:target 0.32 3.74e-04 8.10e-04
## block:sex 0.32 7.07e-03 0.015
## block:sex:target 0.05 2.06e-07 3.70e-06
##
## * Compared among: all models
## * Priors odds: uniform-equalWe do not find sex-related effects. Overall, learning the mirror reversal did not differ between males and females.
Completion time
plotSexCtrlMT()
Next, we test for sex-related effects with completion times across the different trial types. First, we test aligned trials.
sexAlignedMTANOVA()## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Movement time during aligned trials across targets, blocks, and sexes, trained hand:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 sex 1 60 2.2021472 0.1430532306 2.969647e-02
## 3 block 2 120 9.0187512 0.0002244136 * 1.225824e-02
## 5 target 2 120 1.7433813 0.1793289676 1.917954e-03
## 4 sex:block 2 120 0.2656396 0.7671650667 3.654033e-04
## 6 sex:target 2 120 0.9708498 0.3817158057 1.068974e-03
## 7 block:target 4 240 0.2303513 0.9211706842 6.688927e-05
## 8 sex:block:target 4 240 0.3583436 0.8380808119 1.040517e-04
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.3040596 5.588324e-16 *
## 4 sex:block 0.3040596 5.588324e-16 *
## 5 target 0.2836304 7.181339e-17 *
## 6 sex:target 0.2836304 7.181339e-17 *
## 7 block:target 0.6123178 7.450152e-04 *
## 8 sex:block:target 0.6123178 7.450152e-04 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 block 0.5896434 0.002326023 * 0.5944886 0.00226224
## 4 sex:block 0.5896434 0.646734641 0.5944886 0.64864648
## 5 target 0.5826251 0.191315630 0.5870702 0.19126152
## 6 sex:target 0.5826251 0.341125195 0.5870702 0.34174315
## 7 block:target 0.8133906 0.889208922 0.8655491 0.89941463
## 8 sex:block:target 0.8133906 0.799129386 0.8655491 0.81112612
## p[HF]<.05
## 3 *
## 4
## 5
## 6
## 7
## 8## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Movement time during aligned trials across targets, blocks, and sexes, untrained hand:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 sex 1 60 1.89336313 0.17393760 0.0212560059
## 3 block 2 120 3.18926540 0.04471741 * 0.0089489377
## 5 target 2 120 2.09754016 0.12723635 0.0017911183
## 4 sex:block 2 120 1.47278547 0.23340034 0.0041525712
## 6 sex:target 2 120 0.37050764 0.69117076 0.0003168488
## 7 block:target 4 240 0.06558589 0.99205900 0.0000989938
## 8 sex:block:target 4 240 0.49086625 0.74245350 0.0007404267
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.4467670 4.757650e-11 *
## 4 sex:block 0.4467670 4.757650e-11 *
## 5 target 0.9818769 5.830191e-01
## 6 sex:target 0.9818769 5.830191e-01
## 7 block:target 0.2692337 7.714761e-13 *
## 8 sex:block:target 0.2692337 7.714761e-13 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 block 0.6438184 0.06753798 0.6518716 0.06692397
## 4 sex:block 0.6438184 0.23393812 0.6518716 0.23406480
## 5 target 0.9821995 0.12820063 1.0151384 0.12723635
## 6 sex:target 0.9821995 0.68740068 1.0151384 0.69117076
## 7 block:target 0.5886319 0.95674519 0.6142121 0.96121091
## 8 sex:block:target 0.5886319 0.64377365 0.6142121 0.65172485
## p[HF]<.05
## 3
## 4
## 5
## 6
## 7
## 8sexAlignedMTBayesANOVA()## Bayes factor analysis
## --------------
## [1] target + participant : 2.918553 ±2.27%
## [2] block + participant : 140999124 ±0.88%
## [3] target + block + participant : 655126836 ±1.59%
## [4] target + block + target:block + participant : 6613295 ±13.22%
## [5] sex + participant : 0.8570994 ±2.37%
## [6] target + sex + participant : 2.573556 ±4.28%
## [7] block + sex + participant : 130587284 ±7.26%
## [8] target + block + sex + participant : 549427667 ±2.81%
## [9] target + block + target:block + sex + participant : 5128876 ±6.02%
## [10] target + sex + target:sex + participant : 0.4346712 ±3.03%
## [11] target + block + sex + target:sex + participant : 106316019 ±2.32%
## [12] target + block + target:block + sex + target:sex + participant : 967517.9 ±3.89%
## [13] block + sex + block:sex + participant : 10810698 ±10.13%
## [14] target + block + sex + block:sex + participant : 41651175 ±2.62%
## [15] target + block + target:block + sex + block:sex + participant : 387058.5 ±2.81%
## [16] target + block + sex + target:sex + block:sex + participant : 8765883 ±4.72%
## [17] target + block + target:block + sex + target:sex + block:sex + participant : 80209.99 ±5.27%
## [18] target + block + target:block + sex + target:sex + block:sex + target:block:sex + participant : 2276.292 ±4.37%
##
## Against denominator:
## movementtime ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 0.83 1.74
## block 0.74 1.00 7.60e+07
## block:target 0.32 7.95e-03 0.017
## sex 0.74 0.52 0.380
## sex:target 0.32 0.07 0.163
## block:sex 0.32 0.04 0.084
## block:sex:target 0.05 1.37e-06 2.47e-05
##
## * Compared among: all models
## * Priors odds: uniform-equalBayes factor analysis
## --------------
## [1] target + participant : 0.08275806 ±1.37%
## [2] block + participant : 7144.201 ±0.78%
## [3] target + block + participant : 649.031 ±4.49%
## [4] target + block + target:block + participant : 6.592245 ±7.12%
## [5] sex + participant : 0.7164054 ±2.47%
## [6] target + sex + participant : 0.05921556 ±3.91%
## [7] block + sex + participant : 5343.535 ±2.1%
## [8] target + block + sex + participant : 501.1877 ±9.4%
## [9] target + block + target:block + sex + participant : 4.26716 ±1.75%
## [10] target + sex + target:sex + participant : 0.003239597 ±3.58%
## [11] target + block + sex + target:sex + participant : 27.8428 ±11.15%
## [12] target + block + target:block + sex + target:sex + participant : 0.2487787 ±3.56%
## [13] block + sex + block:sex + participant : 5215.027 ±2.47%
## [14] target + block + sex + block:sex + participant : 469.938 ±3.03%
## [15] target + block + target:block + sex + block:sex + participant : 4.407369 ±2.34%
## [16] target + block + sex + target:sex + block:sex + participant : 25.82668 ±4.49%
## [17] target + block + target:block + sex + target:sex + block:sex + participant : 0.2759601 ±7.01%
## [18] target + block + target:block + sex + target:sex + block:sex + target:block:sex + participant : 0.01042376 ±5.81%
##
## Against denominator:
## movementtime ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 0.09 0.034
## block 0.74 1.00 3.72e+03
## block:target 0.32 8.15e-04 0.002
## sex 0.74 0.60 0.531
## sex:target 0.32 2.80e-03 0.006
## block:sex 0.32 0.29 0.905
## block:sex:target 0.05 5.37e-07 9.67e-06
##
## * Compared among: all models
## * Priors odds: uniform-equalWe do not find any effects of sex. We then look into the mirror reversed trials.
sexMirrorMTANOVA()## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 sex 1 60 5.9896694 1.733418e-02 * 0.027182747
## 3 target 2 120 18.0469373 1.405151e-07 * 0.052389471
## 5 block 2 120 27.4560573 1.519432e-10 * 0.096076317
## 4 sex:target 2 120 1.1586491 3.173964e-01 0.003536908
## 6 sex:block 2 120 2.4102089 9.413191e-02 0.009244166
## 7 target:block 4 240 2.7224775 3.022458e-02 * 0.013606899
## 8 sex:target:block 4 240 0.2782311 8.918903e-01 0.001407793
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 target 0.9418537 1.708096e-01
## 4 sex:target 0.9418537 1.708096e-01
## 5 block 0.6152843 5.994272e-07 *
## 6 sex:block 0.6152843 5.994272e-07 *
## 7 target:block 0.2605728 3.233792e-13 *
## 8 sex:target:block 0.2605728 3.233792e-13 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 target 0.9450489 2.795514e-07 * 0.9748422 1.925078e-07
## 4 sex:target 0.9450489 3.155323e-01 0.9748422 3.165718e-01
## 5 block 0.7221699 3.062291e-08 * 0.7352383 2.384339e-08
## 6 sex:block 0.7221699 1.115805e-01 0.7352383 1.107256e-01
## 7 target:block 0.5677428 6.225575e-02 0.5912504 5.983768e-02
## 8 sex:target:block 0.5677428 7.849100e-01 0.5912504 7.934334e-01
## p[HF]<.05
## 3 *
## 4
## 5 *
## 6
## 7
## 8sexMirrorMTBayesANOVA()## Bayes factor analysis
## --------------
## [1] target + participant : 2223146 ±0.85%
## [2] block + participant : 4.326027e+16 ±0.94%
## [3] target + block + participant : 3.412924e+24 ±1.26%
## [4] target + block + target:block + participant : 1.578636e+24 ±1.37%
## [5] sex + participant : 1.833589 ±1.05%
## [6] target + sex + participant : 4233684 ±1.35%
## [7] block + sex + participant : 9.145891e+16 ±1.9%
## [8] target + block + sex + participant : 7.415929e+24 ±1.43%
## [9] target + block + target:block + sex + participant : 3.636149e+24 ±2.41%
## [10] target + sex + target:sex + participant : 478639.9 ±1.27%
## [11] target + block + sex + target:sex + participant : 1.000951e+24 ±1.81%
## [12] target + block + target:block + sex + target:sex + participant : 5.178314e+23 ±2.73%
## [13] block + sex + block:sex + participant : 6.099309e+16 ±1.61%
## [14] target + block + sex + block:sex + participant : 6.568441e+24 ±2.06%
## [15] target + block + target:block + sex + block:sex + participant : 3.415537e+24 ±5.98%
## [16] target + block + sex + target:sex + block:sex + participant : 1.079278e+24 ±13.61%
## [17] target + block + target:block + sex + target:sex + block:sex + participant : 5.021631e+23 ±4.67%
## [18] target + block + target:block + sex + target:sex + block:sex + target:block:sex + participant : 1.600834e+22 ±2.21%
##
## Against denominator:
## movementtime ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 1.00 5.32e+07
## block 0.74 1.00 1.50e+18
## block:target 0.32 0.33 1.08
## sex 0.74 0.83 1.73
## sex:target 0.32 0.11 0.259
## block:sex 0.32 0.40 1.43
## block:sex:target 0.05 5.49e-04 0.010
##
## * Compared among: all models
## * Priors odds: uniform-equalWe find a main effect of sex.
sexMirrorMTComparisons()##
## Welch Two Sample t-test
##
## data: maledat$movementtime and femaledat$movementtime
## t = -2.9857, df = 50.912, p-value = 0.004341
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -2.2282246 -0.4364219
## sample estimates:
## mean of x mean of y
## 3.002728 4.335052
##
## Bayesian t-test (males vs. females):
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 3.118012 ±0.01%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZSFollow up tests show that regardless of target or block, males have faster completion times on average during perturbed reaches.
Finally, we test for washout trials.
sexRAEMTANOVA()## Warning: You have removed one or more levels from variable "block". Refactoring
## for ANOVA.## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Movement time during washout trials across targets, blocks, and sexes, trained hand:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 sex 1 60 4.508826280 3.785353e-02 * 5.435103e-02
## 3 block 1 60 30.725790132 7.014811e-07 * 1.551028e-02
## 5 target 2 120 3.361268454 3.798772e-02 * 5.992622e-03
## 4 sex:block 1 60 4.048671616 4.870218e-02 * 2.071654e-03
## 6 sex:target 2 120 0.032127960 9.683910e-01 5.762118e-05
## 7 block:target 2 120 0.006046689 9.939719e-01 9.754048e-06
## 8 sex:block:target 2 120 0.359008560 6.991159e-01 5.787951e-04
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 5 target 0.9970279 0.9159372
## 6 sex:target 0.9970279 0.9159372
## 7 block:target 0.9351011 0.1381428
## 8 sex:block:target 0.9351011 0.1381428
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 5 target 0.9970367 0.03813335 * 1.0312608 0.03798772
## 6 sex:target 0.9970367 0.96812031 1.0312608 0.96839099
## 7 block:target 0.9390563 0.99205112 0.9683518 0.99304194
## 8 sex:block:target 0.9390563 0.68578941 0.9683518 0.69230775
## p[HF]<.05
## 5 *
## 6
## 7
## 8sexRAEMTBayesANOVA()## Bayes factor analysis
## --------------
## [1] target + participant : 1.932662 ±1.01%
## [2] block + participant : 270516 ±0.99%
## [3] target + block + participant : 814345.5 ±2.28%
## [4] target + block + target:block + participant : 51635.74 ±4%
## [5] sex + participant : 1.824429 ±1.44%
## [6] target + sex + participant : 3.690005 ±2.78%
## [7] block + sex + participant : 516177.5 ±6.48%
## [8] target + block + sex + participant : 1532772 ±3.22%
## [9] target + block + target:block + sex + participant : 97860.62 ±4.04%
## [10] target + sex + target:sex + participant : 0.2564754 ±3.44%
## [11] target + block + sex + target:sex + participant : 102225.8 ±3.83%
## [12] target + block + target:block + sex + target:sex + participant : 6276.998 ±8.48%
## [13] block + sex + block:sex + participant : 302743.2 ±2.39%
## [14] target + block + sex + block:sex + participant : 1136706 ±16.01%
## [15] target + block + target:block + sex + block:sex + participant : 73720.08 ±12.32%
## [16] target + block + sex + target:sex + block:sex + participant : 64492.04 ±3.09%
## [17] target + block + target:block + sex + target:sex + block:sex + participant : 3888.045 ±4.94%
## [18] target + block + target:block + sex + target:sex + block:sex + target:block:sex + participant : 559.9316 ±3.43%
##
## Against denominator:
## movementtime ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 0.78 1.27
## block 0.74 1.00 2.04e+05
## block:target 0.32 0.05 0.107
## sex 0.74 0.77 1.21
## sex:target 0.32 0.04 0.080
## block:sex 0.32 0.32 1.01
## block:sex:target 0.05 1.13e-04 0.002
##
## * Compared among: all models
## * Priors odds: uniform-equalWe find a main effect of sex and a sex x block interaction.
sexRAEMTComparisonsEffSize()## Contrasts set to contr.sum for the following variables: sex## contrast estimate SE df t.ratio p.value
## 1st block: Males vs Females -0.449 0.1930 60 -2.328 0.0699
## 2nd block: Males vs Females -0.306 0.1689 60 -1.811 0.2255
## Last block: Males vs Females -0.169 0.0865 60 -1.955 0.1657
##
## P value adjustment: bonferroni method for 3 tests
## contrast etasquared
## 1 1st block: Males vs Females 0.08282991
## 2 2nd block: Males vs Females 0.05182093
## 3 Last block: Males vs Females 0.05989916sexRAEMTBayesfollowup()## Bayesian t-test block 1, males vs females:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 2.490646 ±0.01%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test block 2, males vs females:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 1.063017 ±0.01%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test last block, males vs females:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 1.321738 ±0.01%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZSFollow-up frequentist tests do not show any significant effects. But Bayesian tests show anecdotal evidence that males continue to move faster after perturbation training. These results suggest that males initiate and execute movements faster than females during perturbed and washout trials, even though no sex differences were observed in aligned baseline reaches.
Path length
plotSexCtrlPL()
We repeat the same tests and use path length as the dependent variable.
sexAlignedPLANOVA()## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Path length during aligned trials across targets, blocks, and sexes, trained hand:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 sex 1 60 0.04799516 0.82733286 0.0004186358
## 3 block 2 120 0.59190991 0.55487671 0.0015089908
## 5 target 2 120 7.27115819 0.00104554 * 0.0157779940
## 4 sex:block 2 120 1.78914909 0.17153082 0.0045473038
## 6 sex:target 2 120 0.59201121 0.55482106 0.0013035226
## 7 block:target 4 240 0.27117840 0.89636587 0.0008623122
## 8 sex:block:target 4 240 1.29914014 0.27103257 0.0041176377
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.8295732 0.004038441 *
## 4 sex:block 0.8295732 0.004038441 *
## 5 target 0.9699288 0.406279674
## 6 sex:target 0.9699288 0.406279674
## 7 block:target 0.7131488 0.019576145 *
## 8 sex:block:target 0.7131488 0.019576145 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 block 0.8543892 0.529537703 0.8769372 0.53371897
## 4 sex:block 0.8543892 0.177210794 0.8769372 0.17636577
## 5 target 0.9708066 0.001185024 * 1.0027699 0.00104554
## 6 sex:target 0.9708066 0.550036732 1.0027699 0.55482106
## 7 block:target 0.8659100 0.872323502 0.9254312 0.88371551
## 8 sex:block:target 0.8659100 0.274160596 0.9254312 0.27284544
## p[HF]<.05
## 3
## 4
## 5 *
## 6
## 7
## 8## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Path length during aligned trials across targets, blocks, and sexes, untrained hand:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 sex 1 60 1.72263552 0.194352779 0.0087593988
## 3 block 2 120 6.40857463 0.002267908 * 0.0166185711
## 5 target 2 120 0.87333916 0.420191733 0.0025962877
## 4 sex:block 2 120 0.77180172 0.464459974 0.0020311078
## 6 sex:target 2 120 0.06131514 0.940556241 0.0001827205
## 7 block:target 4 240 1.13296414 0.341571614 0.0066616595
## 8 sex:block:target 4 240 1.36704257 0.246019135 0.0080269578
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.9540306 0.249510212
## 4 sex:block 0.9540306 0.249510212
## 5 target 0.8504614 0.008410302 *
## 6 sex:target 0.8504614 0.008410302 *
## 7 block:target 0.6301317 0.001416781 *
## 8 sex:block:target 0.6301317 0.001416781 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 block 0.9560509 0.002658413 * 0.9867650 0.002378985
## 4 sex:block 0.9560509 0.459261355 0.9867650 0.462919652
## 5 target 0.8699143 0.407396820 0.8936598 0.409890586
## 6 sex:target 0.8699143 0.920068310 0.8936598 0.924311773
## 7 block:target 0.8048958 0.338516717 0.8559051 0.339564154
## 8 sex:block:target 0.8048958 0.252737839 0.8559051 0.251086272
## p[HF]<.05
## 3 *
## 4
## 5
## 6
## 7
## 8sexAlignedPLBayesANOVA()## Bayes factor analysis
## --------------
## [1] target + participant : 159.5607 ±0.84%
## [2] block + participant : 0.04806725 ±0.78%
## [3] target + block + participant : 7.7941 ±0.89%
## [4] target + block + target:block + participant : 0.06481099 ±1.85%
## [5] sex + participant : 0.2779333 ±0.51%
## [6] target + sex + participant : 44.96409 ±1.37%
## [7] block + sex + participant : 0.01323571 ±0.76%
## [8] target + block + sex + participant : 2.23859 ±1.48%
## [9] target + block + target:block + sex + participant : 0.01785176 ±1.5%
## [10] target + sex + target:sex + participant : 3.626848 ±1.43%
## [11] target + block + sex + target:sex + participant : 0.1792886 ±1.65%
## [12] target + block + target:block + sex + target:sex + participant : 0.001475005 ±3.96%
## [13] block + sex + block:sex + participant : 0.004795714 ±3.88%
## [14] target + block + sex + block:sex + participant : 0.8336562 ±3.47%
## [15] target + block + target:block + sex + block:sex + participant : 0.006714829 ±3.23%
## [16] target + block + sex + target:sex + block:sex + participant : 0.07900986 ±15.92%
## [17] target + block + target:block + sex + target:sex + block:sex + participant : 0.0005400919 ±5.65%
## [18] target + block + target:block + sex + target:sex + block:sex + target:block:sex + participant : 5.535708e-05 ±1.98%
##
## Against denominator:
## pathlength ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 0.99 58.29
## block 0.74 0.05 0.019
## block:target 0.32 4.14e-04 8.98e-04
## sex 0.74 0.24 0.111
## sex:target 0.32 0.02 0.039
## block:sex 0.32 4.19e-03 0.009
## block:sex:target 0.05 2.51e-07 4.51e-06
##
## * Compared among: all models
## * Priors odds: uniform-equalBayes factor analysis
## --------------
## [1] target + participant : 0.04697928 ±0.72%
## [2] block + participant : 3.041801 ±0.67%
## [3] target + block + participant : 0.1487785 ±1.74%
## [4] target + block + target:block + participant : 0.004457703 ±1.55%
## [5] sex + participant : 0.3908647 ±0.83%
## [6] target + sex + participant : 0.01917139 ±2.3%
## [7] block + sex + participant : 1.223754 ±2.64%
## [8] target + block + sex + participant : 0.06137936 ±2.76%
## [9] target + block + target:block + sex + participant : 0.001844853 ±3.44%
## [10] target + sex + target:sex + participant : 0.0008749791 ±1.77%
## [11] target + block + sex + target:sex + participant : 0.003054922 ±5.5%
## [12] target + block + target:block + sex + target:sex + participant : 8.4135e-05 ±2.15%
## [13] block + sex + block:sex + participant : 0.09650413 ±2.08%
## [14] target + block + sex + block:sex + participant : 0.004674154 ±2.53%
## [15] target + block + target:block + sex + block:sex + participant : 0.000144137 ±2.34%
## [16] target + block + sex + target:sex + block:sex + participant : 0.0002348596 ±8.73%
## [17] target + block + target:block + sex + target:sex + block:sex + participant : 6.685839e-06 ±3.37%
## [18] target + block + target:block + sex + target:sex + block:sex + target:block:sex + participant : 1.271624e-06 ±5.28%
##
## Against denominator:
## pathlength ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 0.05 0.018
## block 0.74 0.76 1.12
## block:target 0.32 1.08e-03 0.002
## sex 0.74 0.30 0.152
## sex:target 0.32 7.04e-04 0.002
## block:sex 0.32 0.02 0.037
## block:sex:target 0.05 2.10e-07 3.79e-06
##
## * Compared among: all models
## * Priors odds: uniform-equalWe do not find sex-related effects in the aligned trials. Next, we test for mirror reversed trials.
sexMirrorPLANOVA()## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 sex 1 60 1.98923864 1.635840e-01 5.899935e-03
## 3 target 2 120 16.84584604 3.563291e-07 * 5.507236e-02
## 5 block 2 120 21.45024441 1.085254e-08 * 9.259100e-02
## 4 sex:target 2 120 0.01053895 9.895173e-01 3.646061e-05
## 6 sex:block 2 120 0.69385260 5.016406e-01 3.289801e-03
## 7 target:block 4 240 3.56430419 7.597503e-03 * 1.911156e-02
## 8 sex:target:block 4 240 0.27177039 8.959922e-01 1.483403e-03
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 target 0.9984915 9.564418e-01
## 4 sex:target 0.9984915 9.564418e-01
## 5 block 0.3847823 5.805569e-13 *
## 6 sex:block 0.3847823 5.805569e-13 *
## 7 target:block 0.1616070 8.206911e-19 *
## 8 sex:target:block 0.1616070 8.206911e-19 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 target 0.9984937 3.626262e-07 * 1.0328449 3.563291e-07
## 4 sex:target 0.9984937 9.894543e-01 1.0328449 9.895173e-01
## 5 block 0.6191116 3.302074e-06 * 0.6256755 2.990767e-06
## 6 sex:block 0.6191116 4.369205e-01 0.6256755 4.383413e-01
## 7 target:block 0.6437578 2.075810e-02 * 0.6751284 1.898072e-02
## 8 sex:target:block 0.6437578 8.157610e-01 0.6751284 8.252954e-01
## p[HF]<.05
## 3 *
## 4
## 5 *
## 6
## 7 *
## 8sexMirrorPLBayesANOVA()## Bayes factor analysis
## --------------
## [1] target + participant : 613337.4 ±5.89%
## [2] block + participant : 4.56967e+13 ±1.32%
## [3] target + block + participant : 3.436952e+20 ±1.88%
## [4] target + block + target:block + participant : 7.416839e+20 ±1.3%
## [5] sex + participant : 0.2801933 ±1.17%
## [6] target + sex + participant : 167265.9 ±1.65%
## [7] block + sex + participant : 1.402157e+13 ±3.53%
## [8] target + block + sex + participant : 1.100485e+20 ±2.44%
## [9] target + block + target:block + sex + participant : 2.384404e+20 ±1.77%
## [10] target + sex + target:sex + participant : 7853.389 ±2.87%
## [11] target + block + sex + target:sex + participant : 5.062193e+18 ±2.61%
## [12] target + block + target:block + sex + target:sex + participant : 1.088989e+19 ±1.83%
## [13] block + sex + block:sex + participant : 1.564835e+12 ±1.94%
## [14] target + block + sex + block:sex + participant : 1.30739e+19 ±1.69%
## [15] target + block + target:block + sex + block:sex + participant : 3.361201e+19 ±4.41%
## [16] target + block + sex + target:sex + block:sex + participant : 6.01398e+17 ±1.99%
## [17] target + block + target:block + sex + target:sex + block:sex + participant : 1.372916e+18 ±2.7%
## [18] target + block + target:block + sex + target:sex + block:sex + target:block:sex + participant : 5.08739e+16 ±3.98%
##
## Against denominator:
## pathlength ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 1.00 8.73e+06
## block 0.74 1.00 6.79e+14
## block:target 0.32 0.68 4.71
## sex 0.74 0.28 0.136
## sex:target 0.32 0.01 0.026
## block:sex 0.32 0.03 0.073
## block:sex:target 0.05 3.39e-05 6.11e-04
##
## * Compared among: all models
## * Priors odds: uniform-equalThere are no sex-related effects. Finally, we test for washout trials.
sexRAEPLANOVA()## Warning: You have removed one or more levels from variable "block". Refactoring
## for ANOVA.## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Path length during washout trials across targets, blocks, and sexes, trained hand:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 sex 1 60 0.7856525 0.378956919 0.0048381922
## 3 block 1 60 7.9731922 0.006433612 * 0.0193479645
## 5 target 2 120 0.3712295 0.690675062 0.0017366603
## 4 sex:block 1 60 0.4512855 0.504303603 0.0011154621
## 6 sex:target 2 120 2.3719627 0.097658573 0.0109934569
## 7 block:target 2 120 0.2192692 0.803426566 0.0007269559
## 8 sex:block:target 2 120 1.4828557 0.231117676 0.0048956890
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 5 target 0.9562554 0.2672578
## 6 sex:target 0.9562554 0.2672578
## 7 block:target 0.9668903 0.3703628
## 8 sex:block:target 0.9668903 0.3703628
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF] p[HF]<.05
## 5 target 0.9580888 0.6816858 0.9889745 0.68834962
## 6 sex:target 0.9580888 0.1001503 0.9889745 0.09830931
## 7 block:target 0.9679514 0.7963709 0.9996717 0.80335586
## 8 sex:block:target 0.9679514 0.2315547 0.9996717 0.23112237sexRAEPLBayesANOVA()## Bayes factor analysis
## --------------
## [1] target + participant : 0.04051862 ±1.74%
## [2] block + participant : 9.353379 ±2.49%
## [3] target + block + participant : 0.3725879 ±5.07%
## [4] target + block + target:block + participant : 0.04342221 ±1.79%
## [5] sex + participant : 0.2934577 ±1.26%
## [6] target + sex + participant : 0.0116107 ±1.84%
## [7] block + sex + participant : 2.751157 ±1.69%
## [8] target + block + sex + participant : 0.1133927 ±7.35%
## [9] target + block + target:block + sex + participant : 0.0122228 ±1.74%
## [10] target + sex + target:sex + participant : 0.006854822 ±2.37%
## [11] target + block + sex + target:sex + participant : 0.06788966 ±2.64%
## [12] target + block + target:block + sex + target:sex + participant : 0.008011903 ±3.09%
## [13] block + sex + block:sex + participant : 0.7159587 ±9.36%
## [14] target + block + sex + block:sex + participant : 0.02375865 ±4.05%
## [15] target + block + target:block + sex + block:sex + participant : 0.0028141 ±5.07%
## [16] target + block + sex + target:sex + block:sex + participant : 0.0154448 ±8.96%
## [17] target + block + target:block + sex + target:sex + block:sex + participant : 0.001715232 ±5.19%
## [18] target + block + target:block + sex + target:sex + block:sex + target:block:sex + participant : 0.0006391319 ±17.35%
##
## Against denominator:
## pathlength ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 0.05 0.018
## block 0.74 0.91 3.56
## block:target 0.32 4.64e-03 0.010
## sex 0.74 0.27 0.133
## sex:target 0.32 6.78e-03 0.015
## block:sex 0.32 0.05 0.117
## block:sex:target 0.05 4.31e-05 7.76e-04
##
## * Compared among: all models
## * Priors odds: uniform-equalWe do not find any sex effects. Thus, although males move faster than females, the overall trajectory of their reaches do not differ.
Session 2
We also conducted tests that compared device used and sex for reaches in the second session.
Device used: Mouse vs. trackpad
In session 2, there were less mouse users (N = 9) than trackpad users (n = 39), which is probably contributing to the large variability observed in the plots.
Learning
plotDeviceCtrlGen()
We test for device effects for reaches within each quadrant. We conduct a 3x3x2 (target x block x device) mixed design ANOVA, with target and block as within-subjects factors and device as a between-subjects factor. We repeat this test for quadrants 1, 4, 2, top up quadrant 1 trials, and quadrant 1 trials after switching hands.
deviceLearningGenANOVA()## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Quadrant 1:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 devices 1 46 1.330208 0.254726046 0.003461476
## 3 block 2 92 2.948688 0.057381494 0.014433018
## 5 target 2 92 2.474888 0.089760801 0.010834423
## 4 devices:block 2 92 4.160985 0.018621806 * 0.020246739
## 6 devices:target 2 92 1.256262 0.289553787 0.005529090
## 7 block:target 4 184 1.583587 0.180457867 0.015183372
## 8 devices:block:target 4 184 3.552583 0.008094556 * 0.033430910
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.982793014 6.767003e-01
## 4 devices:block 0.982793014 6.767003e-01
## 5 target 0.092825241 5.922252e-24 *
## 6 devices:target 0.092825241 5.922252e-24 *
## 7 block:target 0.003951147 1.250558e-47 *
## 8 devices:block:target 0.003951147 1.250558e-47 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 block 0.9830841 0.05834923 1.0265959 0.05738149
## 4 devices:block 0.9830841 0.01921712 * 1.0265959 0.01862181
## 5 target 0.5243358 0.12096518 0.5259863 0.12085763
## 6 devices:target 0.5243358 0.27029060 0.5259863 0.27042724
## 7 block:target 0.5041984 0.21057112 0.5274132 0.20937673
## 8 devices:block:target 0.5041984 0.03225865 * 0.5274132 0.03020674
## p[HF]<.05
## 3
## 4 *
## 5
## 6
## 7
## 8 *## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Quadrant 4:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 devices 1 46 0.04872535 0.826273142 1.291908e-04
## 3 block 2 92 0.46301023 0.630844712 2.318659e-03
## 5 target 2 92 5.16511997 0.007482667 * 2.042594e-02
## 4 devices:block 2 92 0.57200009 0.566389682 2.862895e-03
## 6 devices:target 2 92 0.01226795 0.987808614 4.952388e-05
## 7 block:target 4 184 0.57955171 0.677821493 5.779823e-03
## 8 devices:block:target 4 184 0.49254800 0.741215962 4.916408e-03
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.767993721 2.633586e-03 *
## 4 devices:block 0.767993721 2.633586e-03 *
## 5 target 0.100554236 3.581033e-23 *
## 6 devices:target 0.100554236 3.581033e-23 *
## 7 block:target 0.002566977 1.192826e-51 *
## 8 devices:block:target 0.002566977 1.192826e-51 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 block 0.8116842 0.59090316 0.8371333 0.59679797
## 4 devices:block 0.8116842 0.53192084 0.8371333 0.53699867
## 5 target 0.5264694 0.02590876 * 0.5282672 0.02578723
## 6 devices:target 0.5264694 0.92133510 0.5282672 0.92191264
## 7 block:target 0.4272519 0.53646997 0.4420953 0.54203772
## 8 devices:block:target 0.4272519 0.58361539 0.4420953 0.58991168
## p[HF]<.05
## 3
## 4
## 5 *
## 6
## 7
## 8## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Quadrant 2:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 devices 1 46 2.5963688 0.11395017 0.0079277312
## 3 block 2 92 0.8429957 0.43371640 0.0037671041
## 5 target 2 92 4.4487713 0.01431308 * 0.0211985267
## 4 devices:block 2 92 0.5118169 0.60110207 0.0022905518
## 6 devices:target 2 92 4.5259919 0.01334066 * 0.0215585523
## 7 block:target 4 184 0.1997769 0.93822030 0.0018559732
## 8 devices:block:target 4 184 0.1032470 0.98125066 0.0009600489
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.983837166 6.930627e-01
## 4 devices:block 0.983837166 6.930627e-01
## 5 target 0.071224721 1.528242e-26 *
## 6 devices:target 0.071224721 1.528242e-26 *
## 7 block:target 0.007907931 3.522223e-41 *
## 8 devices:block:target 0.007907931 3.522223e-41 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 block 0.9840942 0.43215025 1.0277213 0.43371640
## 4 devices:block 0.9840942 0.59820450 1.0277213 0.60110207
## 5 target 0.5184637 0.03890096 * 0.5197108 0.03880159
## 6 devices:target 0.5184637 0.03729631 * 0.5197108 0.03719824
## 7 block:target 0.5157395 0.82579063 0.5403131 0.83541376
## 8 devices:block:target 0.5157395 0.90727759 0.5403131 0.91489112
## p[HF]<.05
## 3
## 4
## 5 *
## 6 *
## 7
## 8## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Quadrant 1A:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 devices 1 46 0.5082008 0.4795196 0.001478362
## 3 block 2 92 2.0452209 0.1351921 0.009710985
## 5 target 2 92 0.3619086 0.6973329 0.001727559
## 4 devices:block 2 92 0.6428260 0.5281495 0.003072685
## 6 devices:target 2 92 1.6127809 0.2049166 0.007652862
## 7 block:target 4 184 1.2646127 0.2855420 0.011561657
## 8 devices:block:target 4 184 0.5672237 0.6867416 0.005219090
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.987124015 7.470741e-01
## 4 devices:block 0.987124015 7.470741e-01
## 5 target 0.062099394 6.989814e-28 *
## 6 devices:target 0.062099394 6.989814e-28 *
## 7 block:target 0.002865018 1.262857e-50 *
## 8 devices:block:target 0.002865018 1.262857e-50 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 block 0.9872877 0.1358639 1.0312796 0.1351921
## 4 devices:block 0.9872877 0.5262566 1.0312796 0.5281495
## 5 target 0.5160223 0.5570290 0.5171027 0.5574689
## 6 devices:target 0.5160223 0.2108032 0.5171027 0.2108223
## 7 block:target 0.5076160 0.2874178 0.5312303 0.2879784
## 8 devices:block:target 0.5076160 0.5715974 0.5312303 0.5792159
## p[HF]<.05
## 3
## 4
## 5
## 6
## 7
## 8## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Quadrant 1L:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 devices 1 46 0.1781590 0.6749264 0.0006773170
## 3 block 2 92 1.6400652 0.1995870 0.0063146349
## 5 target 2 92 0.1215263 0.8857097 0.0007183433
## 4 devices:block 2 92 1.8310712 0.1660333 0.0070448720
## 6 devices:target 2 92 0.1407921 0.8688567 0.0008321292
## 7 block:target 4 184 0.5749000 0.6811837 0.0046606423
## 8 devices:block:target 4 184 1.0698033 0.3728353 0.0086381048
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.937915844 2.364216e-01
## 4 devices:block 0.937915844 2.364216e-01
## 5 target 0.068033628 5.448560e-27 *
## 6 devices:target 0.068033628 5.448560e-27 *
## 7 block:target 0.002063054 1.087201e-53 *
## 8 devices:block:target 0.002063054 1.087201e-53 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 block 0.9415450 0.2012794 0.9804090 0.2001655
## 4 devices:block 0.9415450 0.1685378 0.9804090 0.1668776
## 5 target 0.5176074 0.7378274 0.5187959 0.7384117
## 6 devices:target 0.5176074 0.7180403 0.5187959 0.7186230
## 7 block:target 0.4630895 0.5521154 0.4816839 0.5586056
## 8 devices:block:target 0.4630895 0.3435267 0.4816839 0.3454901
## p[HF]<.05
## 3
## 4
## 5
## 6
## 7
## 8deviceLearningGenBayesANOVA()## Quadrant 1:
## Bayes factor analysis
## --------------
## [1] target + participant : 0.07946947 ±1.86%
## [2] block + participant : 0.04183764 ±0.93%
## [3] target + block + participant : 0.003179468 ±1.11%
## [4] target + block + target:block + participant : 3.866402e-05 ±2.75%
## [5] devices + participant : 0.253121 ±1.01%
## [6] target + devices + participant : 0.02018202 ±1.58%
## [7] block + devices + participant : 0.01068818 ±1.36%
## [8] target + block + devices + participant : 0.0008151414 ±1.73%
## [9] target + block + target:block + devices + participant : 9.977925e-06 ±4.05%
## [10] target + devices + target:devices + participant : 0.003329108 ±1.9%
## [11] target + block + devices + target:devices + participant : 0.0001366846 ±1.87%
## [12] target + block + target:block + devices + target:devices + participant : 1.588588e-06 ±2.25%
## [13] block + devices + block:devices + participant : 0.02760123 ±3.14%
## [14] target + block + devices + block:devices + participant : 0.002103455 ±2.04%
## [15] target + block + target:block + devices + block:devices + participant : 2.437368e-05 ±3.65%
## [16] target + block + devices + target:devices + block:devices + participant : 0.0003522165 ±2.37%
## [17] target + block + target:block + devices + target:devices + block:devices + participant : 4.047204e-06 ±2.22%
## [18] target + block + target:block + devices + target:devices + block:devices + target:block:devices + participant : 2.497109e-05 ±32.27%
##
## Against denominator:
## percentcomp ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 0.08 0.029
## block 0.74 0.06 0.023
## block:target 0.32 7.18e-05 1.56e-04
## devices 0.74 0.22 0.101
## devices:target 0.32 2.67e-03 0.006
## block:devices 0.32 0.02 0.046
## block:devices:target 0.05 1.73e-05 3.12e-04
##
## * Compared among: all models
## * Priors odds: uniform-equalQuadrant 4:
## Bayes factor analysis
## --------------
## [1] target + participant : 21.00227 ±0.65%
## [2] block + participant : 0.07630002 ±1.28%
## [3] target + block + participant : 1.611017 ±1.22%
## [4] target + block + target:block + participant : 0.0857744 ±1.42%
## [5] devices + participant : 0.1807219 ±1.56%
## [6] target + devices + participant : 3.967308 ±3.17%
## [7] block + devices + participant : 0.01363048 ±1.98%
## [8] target + block + devices + participant : 0.3098113 ±2.42%
## [9] target + block + target:block + devices + participant : 0.01596671 ±1.58%
## [10] target + devices + target:devices + participant : 0.2832044 ±2.11%
## [11] target + block + devices + target:devices + participant : 0.02196663 ±2.4%
## [12] target + block + target:block + devices + target:devices + participant : 0.001228773 ±3.61%
## [13] block + devices + block:devices + participant : 0.001717052 ±2.36%
## [14] target + block + devices + block:devices + participant : 0.04891628 ±23.4%
## [15] target + block + target:block + devices + block:devices + participant : 0.002004319 ±2.45%
## [16] target + block + devices + target:devices + block:devices + participant : 0.002644654 ±3.29%
## [17] target + block + target:block + devices + target:devices + block:devices + participant : 0.0003032622 ±50.23%
## [18] target + block + target:block + devices + target:devices + block:devices + target:block:devices + participant : 1.419759e-05 ±2.69%
##
## Against denominator:
## percentcomp ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 0.96 7.68
## block 0.74 0.08 0.030
## block:target 0.32 3.68e-03 0.008
## devices 0.74 0.17 0.073
## devices:target 0.32 0.01 0.024
## block:devices 0.32 1.94e-03 0.004
## block:devices:target 0.05 4.96e-07 8.93e-06
##
## * Compared among: all models
## * Priors odds: uniform-equalQuadrant 2:
## Bayes factor analysis
## --------------
## [1] target + participant : 0.071479 ±1.27%
## [2] block + participant : 0.03588181 ±0.91%
## [3] target + block + participant : 0.002510187 ±0.98%
## [4] target + block + target:block + participant : 3.397933e-05 ±1.18%
## [5] devices + participant : 0.4043848 ±0.72%
## [6] target + devices + participant : 0.02926521 ±1.9%
## [7] block + devices + participant : 0.01504447 ±1.62%
## [8] target + block + devices + participant : 0.001123279 ±4.66%
## [9] target + block + target:block + devices + participant : 1.392998e-05 ±1.7%
## [10] target + devices + target:devices + participant : 0.1136963 ±7.29%
## [11] target + block + devices + target:devices + participant : 0.004770967 ±16.69%
## [12] target + block + target:block + devices + target:devices + participant : 5.335478e-05 ±3.23%
## [13] block + devices + block:devices + participant : 0.001595337 ±4.02%
## [14] target + block + devices + block:devices + participant : 0.0001086426 ±4.01%
## [15] target + block + target:block + devices + block:devices + participant : 1.473593e-06 ±2.03%
## [16] target + block + devices + target:devices + block:devices + participant : 0.0004119311 ±2.99%
## [17] target + block + target:block + devices + target:devices + block:devices + participant : 5.381661e-06 ±3.1%
## [18] target + block + target:block + devices + target:devices + block:devices + target:block:devices + participant : 2.733266e-07 ±2.29%
##
## Against denominator:
## percentcomp ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 0.13 0.055
## block 0.74 0.04 0.014
## block:target 0.32 6.45e-05 1.40e-04
## devices 0.74 0.34 0.184
## devices:target 0.32 0.07 0.165
## block:devices 0.32 1.26e-03 0.003
## block:devices:target 0.05 1.63e-07 2.93e-06
##
## * Compared among: all models
## * Priors odds: uniform-equalQuadrant 1A:
## Bayes factor analysis
## --------------
## [1] target + participant : 0.2938264 ±0.71%
## [2] block + participant : 0.1088527 ±0.64%
## [3] target + block + participant : 0.03270331 ±1.36%
## [4] target + block + target:block + participant : 0.001287443 ±8.34%
## [5] devices + participant : 0.213913 ±1.03%
## [6] target + devices + participant : 0.06304512 ±1.29%
## [7] block + devices + participant : 0.02307595 ±2.4%
## [8] target + block + devices + participant : 0.01139162 ±36.51%
## [9] target + block + target:block + devices + participant : 0.0002491973 ±2.01%
## [10] target + devices + target:devices + participant : 0.02262911 ±3.36%
## [11] target + block + devices + target:devices + participant : 0.002351005 ±1.95%
## [12] target + block + target:block + devices + target:devices + participant : 9.050788e-05 ±4.4%
## [13] block + devices + block:devices + participant : 0.002726255 ±2.28%
## [14] target + block + devices + block:devices + participant : 0.0007957692 ±1.8%
## [15] target + block + target:block + devices + block:devices + participant : 2.997075e-05 ±4.97%
## [16] target + block + devices + target:devices + block:devices + participant : 0.0002767585 ±2.78%
## [17] target + block + target:block + devices + target:devices + block:devices + participant : 1.020764e-05 ±5.45%
## [18] target + block + target:block + devices + target:devices + block:devices + target:block:devices + participant : 8.325848e-07 ±6.36%
##
## Against denominator:
## percentcomp ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 0.24 0.114
## block 0.74 0.10 0.041
## block:target 0.32 9.39e-04 0.002
## devices 0.74 0.19 0.085
## devices:target 0.32 0.01 0.031
## block:devices 0.32 2.16e-03 0.005
## block:devices:target 0.05 4.68e-07 8.43e-06
##
## * Compared among: all models
## * Priors odds: uniform-equalQuadrant 1L:
## Bayes factor analysis
## --------------
## [1] target + participant : 0.0287211 ±1.32%
## [2] block + participant : 0.08751904 ±0.76%
## [3] target + block + participant : 0.00258294 ±1.83%
## [4] target + block + target:block + participant : 9.729907e-05 ±1.35%
## [5] devices + participant : 0.2100901 ±2.71%
## [6] target + devices + participant : 0.005987374 ±2.99%
## [7] block + devices + participant : 0.01897636 ±3.64%
## [8] target + block + devices + participant : 0.0005083236 ±1.88%
## [9] target + block + target:block + devices + participant : 2.123002e-05 ±2.81%
## [10] target + devices + target:devices + participant : 0.0005003395 ±3.52%
## [11] target + block + devices + target:devices + participant : 4.709667e-05 ±7.6%
## [12] target + block + target:block + devices + target:devices + participant : 1.634614e-06 ±2.62%
## [13] block + devices + block:devices + participant : 0.004761868 ±1.5%
## [14] target + block + devices + block:devices + participant : 0.0001434611 ±2.16%
## [15] target + block + target:block + devices + block:devices + participant : 5.62399e-06 ±2.83%
## [16] target + block + devices + target:devices + block:devices + participant : 1.16483e-05 ±3.7%
## [17] target + block + target:block + devices + target:devices + block:devices + participant : 4.534061e-07 ±2.93%
## [18] target + block + target:block + devices + target:devices + block:devices + target:block:devices + participant : 7.776657e-08 ±2.39%
##
## Against denominator:
## percentcomp ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 0.03 0.010
## block 0.74 0.08 0.033
## block:target 0.32 9.29e-05 2.01e-04
## devices 0.74 0.18 0.077
## devices:target 0.32 4.13e-04 8.95e-04
## block:devices 0.32 3.62e-03 0.008
## block:devices:target 0.05 5.72e-08 1.03e-06
##
## * Compared among: all models
## * Priors odds: uniform-equalWe find a significant target x block x device interaction in quadrant 1, and a significant device x target interaction in quadrant 2. However, both interactions did not hold up in the Bayesian tests.
deviceLearningGenQ1ComparisonsEffSize()## Contrasts set to contr.sum for the following variables: devices## contrast estimate SE df t.ratio p.value
## 1st block, Far: Mouse vs. Trackpad -2.13 17.6 46 -0.121 1.0000
## 1st block, Mid: Mouse vs. Trackpad 4.17 31.2 46 0.134 1.0000
## 1st block, Near: Mouse vs. Trackpad 217.46 170.6 46 1.275 1.0000
## 2nd block, Far: Mouse vs. Trackpad -5.85 13.2 46 -0.442 1.0000
## 2nd block, Mid: Mouse vs. Trackpad 15.18 23.2 46 0.655 1.0000
## 2nd block, Near: Mouse vs. Trackpad -86.39 168.8 46 -0.512 1.0000
## Last block, Far: Mouse vs. Trackpad -15.65 12.0 46 -1.303 1.0000
## Last block, Mid: Mouse vs. Trackpad -22.01 24.3 46 -0.907 1.0000
## Last block, Near: Mouse vs. Trackpad -474.19 186.0 46 -2.550 0.1275
##
## P value adjustment: bonferroni method for 9 tests
## contrast etasquared
## 1 1st block, Far: Mouse vs. Trackpad 0.0003175400
## 2 1st block, Mid: Mouse vs. Trackpad 0.0003892389
## 3 1st block, Near: Mouse vs. Trackpad 0.0341192543
## 4 2nd block, Far: Mouse vs. Trackpad 0.0042369286
## 5 2nd block, Mid: Mouse vs. Trackpad 0.0092533096
## 6 2nd block, Near: Mouse vs. Trackpad 0.0056622865
## 7 Last block, Far: Mouse vs. Trackpad 0.0356188074
## 8 Last block, Mid: Mouse vs. Trackpad 0.0175713290
## 9 Last block, Near: Mouse vs. Trackpad 0.1238458321deviceLearningGenQ1Bayesfollowup()## FIRST BLOCK:
## Bayesian t-test far target, mouse vs. trackpad:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.3494754 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test mid target, mouse vs. trackpad:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.3499077 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test near target, mouse vs. trackpad:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.6373397 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## SECOND BLOCK:
## Bayesian t-test far target, mouse vs. trackpad:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.3739977 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test mid target, mouse vs. trackpad:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.4081957 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test near target, mouse vs. trackpad:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.3833817 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## LAST BLOCK:
## Bayesian t-test far target, mouse vs. trackpad:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.6551173 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test mid target, mouse vs. trackpad:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.4727567 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test near target, mouse vs. trackpad:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 3.792378 ±0.01%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZSFollow-up tests in quadrant 1 show that there are no differences between devices across blocks and targets. However, Bayesian test comparing devices in the near target during the last block show anecdotal evidence for a difference. In the plot, this is seen with how mouse users were over compensating during the last block.
deviceLearningGenQ2ComparisonsEffSize()## Contrasts set to contr.sum for the following variables: devices## contrast estimate SE df t.ratio p.value
## Far: Mouse vs. Trackpad 0.589 12.2 46 0.048 1.0000
## Mid: Mouse vs. Trackpad 18.169 14.1 46 1.290 0.6108
## Near: Mouse vs. Trackpad -183.758 93.1 46 -1.973 0.1637
##
## P value adjustment: bonferroni method for 3 tests
## contrast etasquared
## 1 Far: Mouse vs. Trackpad 5.068625e-05
## 2 Mid: Mouse vs. Trackpad 3.489785e-02
## 3 Near: Mouse vs. Trackpad 7.800233e-02deviceLearningGenQ2Bayesfollowup()## Bayesian t-test far target, mouse vs. trackpad:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.3478715 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test mid target, mouse vs. trackpad:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.6465031 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test near target, mouse vs. trackpad:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 1.471201 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZSFollow-up tests for quadrant 2 show no effects. But, Bayesian follow-up test on the near target show anecdotal evidence of a difference between devices. In the plot, this is again observed with how mouse users are overcompensating.
Next, we check washout trials.
deviceWashoutLearningANOVA()## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Quadrant 1W:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 devices 1 46 0.08261926 7.750697e-01 0.0003181499
## 3 block 2 92 10.74151022 6.418289e-05 * 0.0319004449
## 5 target 2 92 3.40464158 3.745792e-02 * 0.0164102681
## 4 devices:block 2 92 0.40185900 6.702438e-01 0.0012312607
## 6 devices:target 2 92 1.71088674 1.864042e-01 0.0083142983
## 7 block:target 4 184 0.75187744 5.579354e-01 0.0074026893
## 8 devices:block:target 4 184 1.36135098 2.490783e-01 0.0133233771
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.9058906 0.10819439
## 4 devices:block 0.9058906 0.10819439
## 5 target 0.8548781 0.02936596 *
## 6 devices:target 0.8548781 0.02936596 *
## 7 block:target 0.7824046 0.28302520
## 8 devices:block:target 0.7824046 0.28302520
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 block 0.9139854 0.0001154594 * 0.9498616 9.036103e-05
## 4 devices:block 0.9139854 0.6518699397 0.9498616 6.597401e-01
## 5 target 0.8732695 0.0442237316 * 0.9048708 4.243060e-02
## 6 devices:target 0.8732695 0.1906819859 0.9048708 1.896600e-01
## 7 block:target 0.8902629 0.5437754668 0.9741608 5.547372e-01
## 8 devices:block:target 0.8902629 0.2529008689 0.9741608 2.500004e-01
## p[HF]<.05
## 3 *
## 4
## 5 *
## 6
## 7
## 8deviceWashoutLearningBayesANOVA()## Quadrant 1W:
## Bayes factor analysis
## --------------
## [1] target + participant : 0.9517297 ±1.18%
## [2] block + participant : 342.5406 ±0.83%
## [3] target + block + participant : 389.0692 ±1.06%
## [4] target + block + target:block + participant : 21.99868 ±1.43%
## [5] devices + participant : 0.194904 ±0.74%
## [6] target + devices + participant : 0.1993748 ±2.99%
## [7] block + devices + participant : 67.08664 ±1.02%
## [8] target + block + devices + participant : 78.32522 ±2.26%
## [9] target + block + target:block + devices + participant : 4.505605 ±2.27%
## [10] target + devices + target:devices + participant : 0.06052462 ±3.88%
## [11] target + block + devices + target:devices + participant : 26.38378 ±3.14%
## [12] target + block + target:block + devices + target:devices + participant : 1.429981 ±1.7%
## [13] block + devices + block:devices + participant : 6.037101 ±2.21%
## [14] target + block + devices + block:devices + participant : 6.823608 ±2.33%
## [15] target + block + target:block + devices + block:devices + participant : 0.3857767 ±2.47%
## [16] target + block + devices + target:devices + block:devices + participant : 2.243628 ±4.06%
## [17] target + block + target:block + devices + target:devices + block:devices + participant : 0.1233307 ±1.98%
## [18] target + block + target:block + devices + target:devices + block:devices + target:block:devices + participant : 0.04424519 ±4.03%
##
## Against denominator:
## angdev ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 0.56 0.456
## block 0.74 1.00 140.54
## block:target 0.32 0.03 0.067
## devices 0.74 0.20 0.092
## devices:target 0.32 0.03 0.071
## block:devices 0.32 0.02 0.036
## block:devices:target 0.05 4.66e-05 8.39e-04
##
## * Compared among: all models
## * Priors odds: uniform-equalWe do not find any device effects. Thus, it seems that overall learning between mouse and trackpad users are the same, but mouse users tend to overcompensate for the near target.
Completion time
plotDeviceCtrlGenMT()
We conduct the same 3x3x2 mixed design ANOVA with completion time as the dependent variable. We conduct this test for reaches to quadrants 1, 4, 2, top-up quadrant 1 trials, quadrant 1 trials after switching hands, and washout trials.
deviceGenmovementtimeANOVA()## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Quadrant 1:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 devices 1 46 0.4738681 4.946702e-01 0.0051476802
## 3 block 2 92 19.9637500 6.292377e-08 * 0.0557389520
## 5 target 2 92 14.3206476 3.849678e-06 * 0.0520464110
## 4 devices:block 2 92 0.3684162 6.928452e-01 0.0010881542
## 6 devices:target 2 92 0.1424615 8.674119e-01 0.0005458853
## 7 block:target 4 184 8.4807468 2.658594e-06 * 0.0330407298
## 8 devices:block:target 4 184 2.3003942 6.041924e-02 0.0091833872
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.8628752 0.0362101291 *
## 4 devices:block 0.8628752 0.0362101291 *
## 5 target 0.9664270 0.4637711857
## 6 devices:target 0.9664270 0.4637711857
## 7 block:target 0.5085996 0.0004378574 *
## 8 devices:block:target 0.5085996 0.0004378574 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 block 0.8794110 3.139987e-07 * 0.9116465 2.042336e-07
## 4 devices:block 0.8794110 6.658229e-01 0.9116465 6.734108e-01
## 5 target 0.9675175 5.229155e-06 * 1.0092672 3.849678e-06
## 6 devices:target 0.9675175 8.609116e-01 1.0092672 8.674119e-01
## 7 block:target 0.7487597 3.320726e-05 * 0.8066908 1.851112e-05
## 8 devices:block:target 0.7487597 8.012260e-02 0.8066908 7.505375e-02
## p[HF]<.05
## 3 *
## 4
## 5 *
## 6
## 7 *
## 8## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Quadrant 4:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 devices 1 46 0.2343380 6.306226e-01 0.0023688294
## 3 block 2 92 11.2260437 4.340593e-05 * 0.0276790668
## 5 target 2 92 21.1967950 2.684272e-08 * 0.0949135769
## 4 devices:block 2 92 0.1183972 8.884783e-01 0.0003001416
## 6 devices:target 2 92 1.0681142 3.478784e-01 0.0052565027
## 7 block:target 4 184 0.6587037 6.214667e-01 0.0027087588
## 8 devices:block:target 4 184 0.2751536 8.937514e-01 0.0011332898
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.9354328 0.2227321744
## 4 devices:block 0.9354328 0.2227321744
## 5 target 0.9412290 0.2559437200
## 6 devices:target 0.9412290 0.2559437200
## 7 block:target 0.4748189 0.0001307358 *
## 8 devices:block:target 0.4748189 0.0001307358 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 block 0.9393488 6.710403e-05 * 0.9779719 5.084221e-05
## 4 devices:block 0.9393488 8.767739e-01 0.9779719 8.843785e-01
## 5 target 0.9444913 5.882392e-08 * 0.9836792 3.380403e-08
## 6 devices:target 0.9444913 3.450647e-01 0.9836792 3.470785e-01
## 7 block:target 0.7375668 5.763763e-01 0.7936318 5.871447e-01
## 8 devices:block:target 0.7375668 8.400600e-01 0.7936318 8.538308e-01
## p[HF]<.05
## 3 *
## 4
## 5 *
## 6
## 7
## 8## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Quadrant 2:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 devices 1 46 0.01758916 8.950691e-01 0.0001028463
## 3 block 2 92 9.75135981 1.442477e-04 * 0.0345880069
## 5 target 2 92 10.89412416 5.672299e-05 * 0.0489908880
## 4 devices:block 2 92 3.15140486 4.744683e-02 * 0.0114459615
## 6 devices:target 2 92 4.35016451 1.566099e-02 * 0.0201558445
## 7 block:target 4 184 4.45651295 1.843341e-03 * 0.0322954676
## 8 devices:block:target 4 184 2.90214828 2.321516e-02 * 0.0212708934
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.417868667 2.974375e-09 *
## 4 devices:block 0.417868667 2.974375e-09 *
## 5 target 0.500373408 1.714431e-07 *
## 6 devices:target 0.500373408 1.714431e-07 *
## 7 block:target 0.005201721 4.530811e-45 *
## 8 devices:block:target 0.005201721 4.530811e-45 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 block 0.6320588 0.0013701739 * 0.6416943 0.0012912284
## 4 devices:block 0.6320588 0.0716403612 0.6416943 0.0708889384
## 5 target 0.6668327 0.0005783151 * 0.6792842 0.0005299791
## 6 devices:target 0.6668327 0.0305516331 * 0.6792842 0.0297984552
## 7 block:target 0.3001083 0.0327102041 * 0.3036880 0.0322271294
## 8 devices:block:target 0.3001083 0.0872423898 0.3036880 0.0866829351
## p[HF]<.05
## 3 *
## 4
## 5 *
## 6 *
## 7 *
## 8## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Quadrant 1A:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 devices 1 46 1.8926464 1.755658e-01 0.0180247392
## 3 block 2 92 2.9212299 5.888184e-02 0.0105538053
## 5 target 2 92 12.7295572 1.316591e-05 * 0.0531244954
## 4 devices:block 2 92 0.2565872 7.742394e-01 0.0009360076
## 6 devices:target 2 92 1.2737331 2.846721e-01 0.0055825909
## 7 block:target 4 184 0.9470745 4.380101e-01 0.0037570464
## 8 devices:block:target 4 184 2.9710145 2.078023e-02 * 0.0116921442
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.8183893 0.0110052 *
## 4 devices:block 0.8183893 0.0110052 *
## 5 target 0.9821733 0.6671645
## 6 devices:target 0.9821733 0.6671645
## 7 block:target 0.7750367 0.2547823
## 8 devices:block:target 0.7750367 0.2547823
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 block 0.8463024 6.831510e-02 0.8751634 6.644188e-02
## 4 devices:block 0.8463024 7.372079e-01 0.8751634 7.447559e-01
## 5 target 0.9824855 1.522072e-05 * 1.0259292 1.316591e-05
## 6 devices:target 0.9824855 2.844400e-01 1.0259292 2.846721e-01
## 7 block:target 0.8883546 4.306803e-01 0.9718725 4.362629e-01
## 8 devices:block:target 0.8883546 2.587862e-02 * 0.9718725 2.195776e-02
## p[HF]<.05
## 3
## 4
## 5 *
## 6
## 7
## 8 *## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Quadrant 1L:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 devices 1 46 0.02252572 8.813532e-01 0.0001545233
## 3 block 2 92 4.77795157 1.061212e-02 * 0.0197046957
## 5 target 2 92 13.98615860 4.971780e-06 * 0.0519638080
## 4 devices:block 2 92 0.89423697 4.124435e-01 0.0037479425
## 6 devices:target 2 92 3.43404440 3.644665e-02 * 0.0132793774
## 7 block:target 4 184 2.29623624 6.081431e-02 0.0152679329
## 8 devices:block:target 4 184 1.32767623 2.612832e-01 0.0088850891
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.8400869 1.982873e-02 *
## 4 devices:block 0.8400869 1.982873e-02 *
## 5 target 0.7591667 2.030422e-03 *
## 6 devices:target 0.7591667 2.030422e-03 *
## 7 block:target 0.1709430 3.480640e-13 *
## 8 devices:block:target 0.1709430 3.480640e-13 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 block 0.8621336 1.461884e-02 * 0.8925945 1.361842e-02
## 4 devices:block 0.8621336 3.995833e-01 0.8925945 4.026251e-01
## 5 target 0.8059100 2.970727e-05 * 0.8308016 2.360736e-05
## 6 devices:target 0.8059100 4.718759e-02 * 0.8308016 4.565253e-02
## 7 block:target 0.5062146 1.056520e-01 0.5296648 1.029493e-01
## 8 devices:block:target 0.5062146 2.701794e-01 0.5296648 2.703196e-01
## p[HF]<.05
## 3 *
## 4
## 5 *
## 6 *
## 7
## 8## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Quadrant 1W:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 devices 1 46 0.09223208 7.627279e-01 0.0007944006
## 3 block 2 92 48.46373213 4.213720e-15 * 0.0937031397
## 5 target 2 92 3.15511683 4.728230e-02 * 0.0117658444
## 4 devices:block 2 92 0.34028035 7.124626e-01 0.0007254183
## 6 devices:target 2 92 0.52692747 5.921873e-01 0.0019844308
## 7 block:target 4 184 2.41755540 5.025228e-02 0.0171373687
## 8 devices:block:target 4 184 0.30007200 8.776257e-01 0.0021595410
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.8808858 5.763567e-02
## 4 devices:block 0.8808858 5.763567e-02
## 5 target 0.7375330 1.059456e-03 *
## 6 devices:target 0.7375330 1.059456e-03 *
## 7 block:target 0.1113585 5.550718e-17 *
## 8 devices:block:target 0.1113585 5.550718e-17 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 block 0.8935639 9.579026e-14 * 0.9272752 3.559950e-14
## 4 devices:block 0.8935639 6.883389e-01 0.9272752 6.963034e-01
## 5 target 0.7920999 5.980682e-02 0.8156714 5.824123e-02
## 6 devices:target 0.7920999 5.511118e-01 0.8156714 5.562547e-01
## 7 block:target 0.5075606 9.388441e-02 0.5311684 9.112656e-02
## 8 devices:block:target 0.5075606 7.447361e-01 0.5311684 7.545234e-01
## p[HF]<.05
## 3 *
## 4
## 5
## 6
## 7
## 8deviceGenmovementtimeBayesANOVA()## Quadrant 1:
## Bayes factor analysis
## --------------
## [1] target + participant : 370790257 ±0.74%
## [2] block + participant : 668741383 ±2.54%
## [3] target + block + participant : 8.017007e+18 ±1.39%
## [4] target + block + target:block + participant : 3.754857e+20 ±2.15%
## [5] devices + participant : 0.3564555 ±0.69%
## [6] target + devices + participant : 141493937 ±2.26%
## [7] block + devices + participant : 254693568 ±0.95%
## [8] target + block + devices + participant : 3.273875e+18 ±2.39%
## [9] target + block + target:block + devices + participant : 1.500962e+20 ±2.48%
## [10] target + devices + target:devices + participant : 11372005 ±2.61%
## [11] target + block + devices + target:devices + participant : 2.624272e+17 ±1.62%
## [12] target + block + target:block + devices + target:devices + participant : 1.272026e+19 ±4.2%
## [13] block + devices + block:devices + participant : 23064351 ±1.54%
## [14] target + block + devices + block:devices + participant : 3.028719e+17 ±2.57%
## [15] target + block + target:block + devices + block:devices + participant : 1.405849e+19 ±2.05%
## [16] target + block + devices + target:devices + block:devices + participant : 2.402409e+16 ±2.07%
## [17] target + block + target:block + devices + target:devices + block:devices + participant : 1.202835e+18 ±6.62%
## [18] target + block + target:block + devices + target:devices + block:devices + target:block:devices + participant : 2.58771e+17 ±2.81%
##
## Against denominator:
## movementtime ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 1.00 2.13e+11
## block 0.74 1.00 3.86e+11
## block:target 0.32 0.98 101.00
## devices 0.74 0.32 0.170
## devices:target 0.32 0.03 0.057
## block:devices 0.32 0.03 0.062
## block:devices:target 0.05 4.57e-04 0.008
##
## * Compared among: all models
## * Priors odds: uniform-equalQuadrant 4:
## Bayes factor analysis
## --------------
## [1] target + participant : 4.88044e+14 ±0.76%
## [2] block + participant : 1056.358 ±0.88%
## [3] target + block + participant : 5.933476e+18 ±1.78%
## [4] target + block + target:block + participant : 2.432169e+17 ±1.14%
## [5] devices + participant : 0.3171937 ±1.29%
## [6] target + devices + participant : 1.62714e+14 ±1.08%
## [7] block + devices + participant : 339.6452 ±1.22%
## [8] target + block + devices + participant : 2.086428e+18 ±2.92%
## [9] target + block + target:block + devices + participant : 8.740663e+16 ±1.73%
## [10] target + devices + target:devices + participant : 4.11696e+13 ±1.69%
## [11] target + block + devices + target:devices + participant : 5.350981e+17 ±1.71%
## [12] target + block + target:block + devices + target:devices + participant : 2.427873e+16 ±2.23%
## [13] block + devices + block:devices + participant : 25.31842 ±2.94%
## [14] target + block + devices + block:devices + participant : 1.541016e+17 ±2.26%
## [15] target + block + target:block + devices + block:devices + participant : 7.021253e+15 ±5.82%
## [16] target + block + devices + target:devices + block:devices + participant : 4.021968e+16 ±1.88%
## [17] target + block + target:block + devices + target:devices + block:devices + participant : 1.754947e+15 ±2.33%
## [18] target + block + target:block + devices + target:devices + block:devices + target:block:devices + participant : 1.336114e+14 ±10.53%
##
## Against denominator:
## movementtime ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 1.00 2.29e+15
## block 0.74 1.00 4.70e+03
## block:target 0.32 0.04 0.090
## devices 0.74 0.32 0.170
## devices:target 0.32 0.07 0.153
## block:devices 0.32 0.02 0.049
## block:devices:target 0.05 1.47e-05 2.64e-04
##
## * Compared among: all models
## * Priors odds: uniform-equalQuadrant 2:
## Bayes factor analysis
## --------------
## [1] target + participant : 356.8195 ±0.92%
## [2] block + participant : 5.037736 ±0.63%
## [3] target + block + participant : 2365.992 ±1.37%
## [4] target + block + target:block + participant : 365.269 ±2.14%
## [5] devices + participant : 0.2183374 ±0.8%
## [6] target + devices + participant : 78.62684 ±1.14%
## [7] block + devices + participant : 1.108652 ±1.23%
## [8] target + block + devices + participant : 538.9632 ±2.32%
## [9] target + block + target:block + devices + participant : 81.77227 ±2.17%
## [10] target + devices + target:devices + participant : 265.0244 ±1.66%
## [11] target + block + devices + target:devices + participant : 2007.891 ±1.85%
## [12] target + block + target:block + devices + target:devices + participant : 330.726 ±2.34%
## [13] block + devices + block:devices + participant : 0.546119 ±1.31%
## [14] target + block + devices + block:devices + participant : 320.852 ±4.93%
## [15] target + block + target:block + devices + block:devices + participant : 49.80932 ±3.13%
## [16] target + block + devices + target:devices + block:devices + participant : 1163.274 ±2.03%
## [17] target + block + target:block + devices + target:devices + block:devices + participant : 193.3367 ±4.5%
## [18] target + block + target:block + devices + target:devices + block:devices + target:block:devices + participant : 130.9973 ±3.12%
##
## Against denominator:
## movementtime ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 1.00 372.43
## block 0.74 0.92 3.85
## block:target 0.32 0.14 0.351
## devices 0.74 0.63 0.596
## devices:target 0.32 0.50 2.13
## block:devices 0.32 0.23 0.629
## block:devices:target 0.05 0.02 0.290
##
## * Compared among: all models
## * Priors odds: uniform-equalQuadrant 1A:
## Bayes factor analysis
## --------------
## [1] target + participant : 18771451139 ±4.69%
## [2] block + participant : 0.5612975 ±0.71%
## [3] target + block + participant : 16902689820 ±2.13%
## [4] target + block + target:block + participant : 435724729 ±1.76%
## [5] devices + participant : 0.6040588 ±0.92%
## [6] target + devices + participant : 12860494250 ±8.4%
## [7] block + devices + participant : 0.3578497 ±2.38%
## [8] target + block + devices + participant : 10738389723 ±2.05%
## [9] target + block + target:block + devices + participant : 281453549 ±2.14%
## [10] target + devices + target:devices + participant : 3933994717 ±2.17%
## [11] target + block + devices + target:devices + participant : 3841136613 ±2.21%
## [12] target + block + target:block + devices + target:devices + participant : 102437675 ±4.23%
## [13] block + devices + block:devices + participant : 0.02881722 ±1.61%
## [14] target + block + devices + block:devices + participant : 873144073 ±2.18%
## [15] target + block + target:block + devices + block:devices + participant : 22991899 ±2.34%
## [16] target + block + devices + target:devices + block:devices + participant : 332675498 ±4.69%
## [17] target + block + target:block + devices + target:devices + block:devices + participant : 8994686 ±3.69%
## [18] target + block + target:block + devices + target:devices + block:devices + target:block:devices + participant : 4759463 ±2.15%
##
## Against denominator:
## movementtime ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 1.00 9.67e+09
## block 0.74 0.49 0.337
## block:target 0.32 0.01 0.027
## devices 0.74 0.48 0.326
## devices:target 0.32 0.12 0.293
## block:devices 0.32 0.02 0.040
## block:devices:target 0.05 6.89e-05 0.001
##
## * Compared among: all models
## * Priors odds: uniform-equalQuadrant 1L:
## Bayes factor analysis
## --------------
## [1] target + participant : 38114.84 ±0.81%
## [2] block + participant : 86.04871 ±0.93%
## [3] target + block + participant : 6762617 ±11.76%
## [4] target + block + target:block + participant : 3911477 ±6.44%
## [5] devices + participant : 0.2382748 ±1.13%
## [6] target + devices + participant : 9415.603 ±2.59%
## [7] block + devices + participant : 21.3226 ±3.14%
## [8] target + block + devices + participant : 2349656 ±35.27%
## [9] target + block + target:block + devices + participant : 955211.6 ±6.04%
## [10] target + devices + target:devices + participant : 9871.735 ±1.95%
## [11] target + block + devices + target:devices + participant : 1780682 ±3.4%
## [12] target + block + target:block + devices + target:devices + participant : 1124387 ±1.96%
## [13] block + devices + block:devices + participant : 3.3615 ±1.73%
## [14] target + block + devices + block:devices + participant : 256515.3 ±1.54%
## [15] target + block + target:block + devices + block:devices + participant : 159540.9 ±3.42%
## [16] target + block + devices + target:devices + block:devices + participant : 333139.6 ±5.72%
## [17] target + block + target:block + devices + target:devices + block:devices + participant : 202856.7 ±4.08%
## [18] target + block + target:block + devices + target:devices + block:devices + target:block:devices + participant : 41520.66 ±3.19%
##
## Against denominator:
## movementtime ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 1.00 5.72e+04
## block 0.74 1.00 111.23
## block:target 0.32 0.36 1.20
## devices 0.74 0.40 0.241
## devices:target 0.32 0.19 0.524
## block:devices 0.32 0.06 0.127
## block:devices:target 0.05 2.32e-03 0.042
##
## * Compared among: all models
## * Priors odds: uniform-equalQuadrant 1W:
## Bayes factor analysis
## --------------
## [1] target + participant : 3.940588 ±0.92%
## [2] block + participant : 2.12497e+17 ±2.58%
## [3] target + block + participant : 2.994102e+18 ±1.55%
## [4] target + block + target:block + participant : 2.479047e+20 ±1.38%
## [5] devices + participant : 0.2679569 ±1.51%
## [6] target + devices + participant : 1.01989 ±1.06%
## [7] block + devices + participant : 5.706466e+16 ±1.21%
## [8] target + block + devices + participant : 8.95826e+17 ±4.27%
## [9] target + block + target:block + devices + participant : 7.301528e+19 ±1.94%
## [10] target + devices + target:devices + participant : 0.1130374 ±1.3%
## [11] target + block + devices + target:devices + participant : 1.0433e+17 ±2.01%
## [12] target + block + target:block + devices + target:devices + participant : 9.298122e+18 ±3.12%
## [13] block + devices + block:devices + participant : 5.193544e+15 ±1.33%
## [14] target + block + devices + block:devices + participant : 5.214754e+17 ±85.56%
## [15] target + block + target:block + devices + block:devices + participant : 6.744291e+18 ±1.93%
## [16] target + block + devices + target:devices + block:devices + participant : 9.760656e+15 ±2.59%
## [17] target + block + target:block + devices + target:devices + block:devices + participant : 8.664705e+17 ±2.98%
## [18] target + block + target:block + devices + target:devices + block:devices + target:block:devices + participant : 8.460297e+16 ±2.6%
##
## Against denominator:
## movementtime ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 1.00 445.12
## block 0.74 1.00 1.93e+19
## block:target 0.32 0.99 152.52
## devices 0.74 0.27 0.130
## devices:target 0.32 0.03 0.068
## block:devices 0.32 0.02 0.053
## block:devices:target 0.05 2.47e-04 0.004
##
## * Compared among: all models
## * Priors odds: uniform-equalWe find a device x target interaction for quadrants 2 and quadrant 1 after switching hands (1L). We also find a target x block x device interaction for quadrant 1 top-up trials (1A).
deviceMTGenQ2ComparisonsEffSize()## Contrasts set to contr.sum for the following variables: devices## contrast estimate SE df t.ratio p.value
## Far: Mouse vs. Trackpad 0.281 0.217 46 1.298 0.6027
## Mid: Mouse vs. Trackpad -0.810 0.645 46 -1.257 0.6448
## Near: Mouse vs. Trackpad 0.662 0.372 46 1.780 0.2449
##
## P value adjustment: bonferroni method for 3 tests
## contrast etasquared
## 1 Far: Mouse vs. Trackpad 0.03530894
## 2 Mid: Mouse vs. Trackpad 0.03323124
## 3 Near: Mouse vs. Trackpad 0.06446458deviceMTGenQ2Bayesfollowup()## Bayesian t-test far target, mouse vs. trackpad:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.6513996 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test mid target, mouse vs. trackpad:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.6270623 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test near target, mouse vs. trackpad:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 1.128575 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZSQuadrant 2 follow-up tests only show anecdotal evidence of a device effect for the near target.
deviceMTGenQ1LComparisonsEffSize()## Contrasts set to contr.sum for the following variables: devices## contrast estimate SE df t.ratio p.value
## Far: Mouse vs. Trackpad 0.0858 0.314 46 0.273 1.0000
## Mid: Mouse vs. Trackpad -0.6877 0.525 46 -1.309 0.5910
## Near: Mouse vs. Trackpad 0.4494 0.407 46 1.104 0.8263
##
## P value adjustment: bonferroni method for 3 tests
## contrast etasquared
## 1 Far: Mouse vs. Trackpad 0.001621018
## 2 Mid: Mouse vs. Trackpad 0.035919494
## 3 Near: Mouse vs. Trackpad 0.025801706deviceMTGenQ1LBayesfollowup()## Bayesian t-test far target, mouse vs. trackpad:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.357428 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test mid target, mouse vs. trackpad:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.6587471 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test near target, mouse vs. trackpad:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.5478735 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZSFollow-up tests for Quadrant 1 after switching hands did not reveal any device effects.
deviceMTGenQ1AComparisonsEffSize()## Contrasts set to contr.sum for the following variables: devices## contrast estimate SE df t.ratio p.value
## 1st block, Far: Mouse vs. Trackpad 0.172 0.211 46 0.816 1.0000
## 1st block, Mid: Mouse vs. Trackpad 0.211 0.380 46 0.554 1.0000
## 1st block, Near: Mouse vs. Trackpad 0.284 0.400 46 0.711 1.0000
## 2nd block, Far: Mouse vs. Trackpad 0.311 0.165 46 1.882 0.5960
## 2nd block, Mid: Mouse vs. Trackpad -0.320 0.357 46 -0.894 1.0000
## 2nd block, Near: Mouse vs. Trackpad 0.902 0.413 46 2.182 0.3080
## Last block, Far: Mouse vs. Trackpad 0.249 0.175 46 1.424 1.0000
## Last block, Mid: Mouse vs. Trackpad 0.511 0.392 46 1.303 1.0000
## Last block, Near: Mouse vs. Trackpad 0.410 0.350 46 1.172 1.0000
##
## P value adjustment: bonferroni method for 9 tests
## contrast etasquared
## 1 1st block, Far: Mouse vs. Trackpad 0.014266646
## 2 1st block, Mid: Mouse vs. Trackpad 0.006632486
## 3 1st block, Near: Mouse vs. Trackpad 0.010878875
## 4 2nd block, Far: Mouse vs. Trackpad 0.071467462
## 5 2nd block, Mid: Mouse vs. Trackpad 0.017092179
## 6 2nd block, Near: Mouse vs. Trackpad 0.093821590
## 7 Last block, Far: Mouse vs. Trackpad 0.042234612
## 8 Last block, Mid: Mouse vs. Trackpad 0.035597195
## 9 Last block, Near: Mouse vs. Trackpad 0.028982434deviceMTGenQ1ABayesfollowup()## FIRST BLOCK:
## Bayesian t-test far target, mouse vs. trackpad:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.4458497 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test mid target, mouse vs. trackpad:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.3899175 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test near target, mouse vs. trackpad:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.4200063 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## SECOND BLOCK:
## Bayesian t-test far target, mouse vs. trackpad:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 1.29343 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test mid target, mouse vs. trackpad:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.4687469 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test near target, mouse vs. trackpad:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 2.022082 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## LAST BLOCK:
## Bayesian t-test far target, mouse vs. trackpad:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.7403178 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test mid target, mouse vs. trackpad:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.6548573 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZS
##
## Bayesian t-test near target, mouse vs. trackpad:
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.5803437 ±0%
##
## Against denominator:
## Null, mu1-mu2 = 0
## ---
## Bayes factor type: BFindepSample, JZSFollow-up tests on quadrant 1 top-up trials only show anecdotal evidence of a device effect for the far target in the second block, and the near target in the second block. In both cases, we see in the plot that these are when mouse users were moving a bit faster than trackpad users. Thus, there is only a small amount of evidence showing that mouse users initiate and execute movements faster than trackpad users.
Path length
plotDeviceCtrlGenPL()
We repeat the same tests and have path length as the dependent variable.
deviceGenpathlengthANOVA()## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Quadrant 1:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 devices 1 46 0.005693493 9.401797e-01 3.601462e-05
## 3 block 2 92 24.465833424 3.018874e-09 * 7.278182e-02
## 5 target 2 92 12.603567382 1.453295e-05 * 4.995583e-02
## 4 devices:block 2 92 2.431198222 9.356220e-02 7.739750e-03
## 6 devices:target 2 92 0.091238382 9.128826e-01 3.805057e-04
## 7 block:target 4 184 5.469689437 3.495183e-04 * 4.208841e-02
## 8 devices:block:target 4 184 0.931441335 4.468902e-01 7.426644e-03
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.9828341 6.773370e-01
## 4 devices:block 0.9828341 6.773370e-01
## 5 target 0.9156023 1.375322e-01
## 6 devices:target 0.9156023 1.375322e-01
## 7 block:target 0.3488107 4.412479e-07 *
## 8 devices:block:target 0.3488107 4.412479e-07 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 block 0.9831238 3.969633e-09 * 1.0266401 3.018874e-09
## 4 devices:block 0.9831238 9.457449e-02 1.0266401 9.356220e-02
## 5 target 0.9221709 2.750289e-05 * 0.9589265 2.034572e-05
## 6 devices:target 0.9221709 8.990852e-01 0.9589265 9.058794e-01
## 7 block:target 0.6956489 1.890690e-03 * 0.7449660 1.435291e-03
## 8 devices:block:target 0.6956489 4.221016e-01 0.7449660 4.269312e-01
## p[HF]<.05
## 3 *
## 4
## 5 *
## 6
## 7 *
## 8## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Quadrant 4:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 devices 1 46 0.04717119 8.290213e-01 0.0003308386
## 3 block 2 92 6.22659739 2.909649e-03 * 0.0209652026
## 5 target 2 92 25.52178196 1.522991e-09 * 0.1098435096
## 4 devices:block 2 92 0.92806668 3.989861e-01 0.0031815985
## 6 devices:target 2 92 1.12403244 3.293880e-01 0.0054053276
## 7 block:target 4 184 1.76514612 1.377001e-01 0.0112554566
## 8 devices:block:target 4 184 0.88329227 4.750538e-01 0.0056641647
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.9474348 2.967292e-01
## 4 devices:block 0.9474348 2.967292e-01
## 5 target 0.9080946 1.142746e-01
## 6 devices:target 0.9080946 1.142746e-01
## 7 block:target 0.4051923 7.335101e-06 *
## 8 devices:block:target 0.4051923 7.335101e-06 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 block 0.9500599 3.450673e-03 * 0.9898625 3.012060e-03
## 4 devices:block 0.9500599 3.949751e-01 0.9898625 3.981923e-01
## 5 target 0.9158303 6.312068e-09 * 0.9519041 3.430971e-09
## 6 devices:target 0.9158303 3.259253e-01 0.9519041 3.274821e-01
## 7 block:target 0.6860138 1.618634e-01 0.7338333 1.580032e-01
## 8 devices:block:target 0.6860138 4.440754e-01 0.7338333 4.497096e-01
## p[HF]<.05
## 3 *
## 4
## 5 *
## 6
## 7
## 8## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Quadrant 2:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 devices 1 46 0.1096892 0.7420023849 0.0009098027
## 3 block 2 92 3.3118029 0.0408431980 * 0.0112149278
## 5 target 2 92 8.1976286 0.0005293796 * 0.0355530095
## 4 devices:block 2 92 1.3845076 0.2556154836 0.0047192290
## 6 devices:target 2 92 0.5911812 0.5557622971 0.0026514130
## 7 block:target 4 184 0.6084793 0.6570231867 0.0033448910
## 8 devices:block:target 4 184 0.8368743 0.5033486187 0.0045946395
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.9628809 0.42695617
## 4 devices:block 0.9628809 0.42695617
## 5 target 0.9264571 0.17929550
## 6 devices:target 0.9264571 0.17929550
## 7 block:target 0.6311062 0.01543016 *
## 8 devices:block:target 0.6311062 0.01543016 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 block 0.9642095 0.0427028303 * 1.0055878 0.0408431980
## 4 devices:block 0.9642095 0.2556824719 1.0055878 0.2556154836
## 5 target 0.9314951 0.0007412512 * 0.9692608 0.0006156366
## 6 devices:target 0.9314951 0.5443419422 0.9692608 0.5507329368
## 7 block:target 0.8282292 0.6265220392 0.9001967 0.6399694667
## 8 devices:block:target 0.8282292 0.4853422939 0.9001967 0.4933095630
## p[HF]<.05
## 3 *
## 4
## 5 *
## 6
## 7
## 8## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Quadrant 1A:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 devices 1 46 0.2928023 0.5910413717 0.0028057463
## 3 block 2 92 4.4973195 0.0136935886 * 0.0166229409
## 5 target 2 92 9.2128940 0.0002254222 * 0.0372658269
## 4 devices:block 2 92 0.1346445 0.8741984485 0.0005058282
## 6 devices:target 2 92 1.0570407 0.3516641440 0.0044215599
## 7 block:target 4 184 2.3423662 0.0565673989 0.0096721962
## 8 devices:block:target 4 184 2.1882015 0.0719961221 0.0090413686
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.8477415 0.02431801 *
## 4 devices:block 0.8477415 0.02431801 *
## 5 target 0.8552974 0.02969173 *
## 6 devices:target 0.8552974 0.02969173 *
## 7 block:target 0.7596980 0.20218717
## 8 devices:block:target 0.7596980 0.20218717
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 block 0.8678608 0.0181041181 * 0.8989068 0.016953064
## 4 devices:block 0.8678608 0.8457718394 0.8989068 0.853065219
## 5 target 0.8735893 0.0004625928 * 0.9052236 0.000386314
## 6 devices:target 0.8735893 0.3445492303 0.9052236 0.346477549
## 7 block:target 0.8695411 0.0659008193 0.9493577 0.060013913
## 8 devices:block:target 0.8695411 0.0818963668 0.9493577 0.075681179
## p[HF]<.05
## 3 *
## 4
## 5 *
## 6
## 7
## 8## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Quadrant 1L:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 devices 1 46 3.7835062 0.0578873022 0.026442801
## 3 block 2 92 7.6909283 0.0008154893 * 0.021929049
## 5 target 2 92 9.5678918 0.0001678649 * 0.045056405
## 4 devices:block 2 92 0.1289765 0.8791532754 0.000375853
## 6 devices:target 2 92 0.3124067 0.7324569726 0.001538206
## 7 block:target 4 184 3.6377960 0.0070444378 * 0.023841177
## 8 devices:block:target 4 184 1.7285560 0.1454777373 0.011472057
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.8508093 0.026376967 *
## 4 devices:block 0.8508093 0.026376967 *
## 5 target 0.8840277 0.062442697
## 6 devices:target 0.8840277 0.062442697
## 7 block:target 0.5527257 0.001814325 *
## 8 devices:block:target 0.5527257 0.001814325 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 block 0.8701776 0.0014692332 * 0.9014611 0.001274583
## 4 devices:block 0.8701776 0.8516358612 0.9014611 0.858872175
## 5 target 0.8960796 0.0003115777 * 0.9300554 0.000254474
## 6 devices:target 0.8960796 0.7085849757 0.9300554 0.716719040
## 7 block:target 0.7612404 0.0140193028 * 0.8212843 0.011778746
## 8 devices:block:target 0.7612404 0.1631252481 0.8212843 0.158542492
## p[HF]<.05
## 3 *
## 4
## 5 *
## 6
## 7 *
## 8## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Quadrant 1W:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 devices 1 46 1.300527 2.600199e-01 0.005827370
## 3 block 2 92 33.819146 9.770904e-12 * 0.123246072
## 5 target 2 92 7.646321 8.472717e-04 * 0.033297974
## 4 devices:block 2 92 1.395029 2.530183e-01 0.005765074
## 6 devices:target 2 92 1.174315 3.136192e-01 0.005262180
## 7 block:target 4 184 4.934610 8.408801e-04 * 0.040577281
## 8 devices:block:target 4 184 1.209408 3.083371e-01 0.010259218
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.24107814 1.254732e-14 *
## 4 devices:block 0.24107814 1.254732e-14 *
## 5 target 0.71427890 5.152595e-04 *
## 6 devices:target 0.71427890 5.152595e-04 *
## 7 block:target 0.05407965 1.702091e-23 *
## 8 devices:block:target 0.05407965 1.702091e-23 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 block 0.5685301 1.213412e-07 * 0.5733221 1.092250e-07
## 4 devices:block 0.5685301 2.471466e-01 0.5733221 2.473498e-01
## 5 target 0.7777737 2.307583e-03 * 0.7999955 2.086804e-03
## 6 devices:target 0.7777737 3.050967e-01 0.7999955 3.061784e-01
## 7 block:target 0.5412987 7.534059e-03 * 0.5689780 6.587372e-03
## 8 devices:block:target 0.5412987 3.047518e-01 0.5689780 3.056659e-01
## p[HF]<.05
## 3 *
## 4
## 5 *
## 6
## 7 *
## 8deviceGenpathlengthBayesANOVA()## Quadrant 1:
## Bayes factor analysis
## --------------
## [1] target + participant : 182340.3 ±0.92%
## [2] block + participant : 3057695 ±1.34%
## [3] target + block + participant : 2.932759e+12 ±1.14%
## [4] target + block + target:block + participant : 6.740723e+14 ±1.68%
## [5] devices + participant : 0.2190031 ±1.08%
## [6] target + devices + participant : 41636.32 ±4.09%
## [7] block + devices + participant : 716772.6 ±2.65%
## [8] target + block + devices + participant : 672831793920 ±1.39%
## [9] target + block + target:block + devices + participant : 1.632859e+14 ±3.39%
## [10] target + devices + target:devices + participant : 3155.751 ±2.68%
## [11] target + block + devices + target:devices + participant : 51925063447 ±3.55%
## [12] target + block + target:block + devices + target:devices + participant : 1.229193e+13 ±5.83%
## [13] block + devices + block:devices + participant : 176012.4 ±1.65%
## [14] target + block + devices + block:devices + participant : 207607500213 ±2.63%
## [15] target + block + target:block + devices + block:devices + participant : 5.029645e+13 ±1.86%
## [16] target + block + devices + target:devices + block:devices + participant : 14560888649 ±2.06%
## [17] target + block + target:block + devices + target:devices + block:devices + participant : 3.601471e+12 ±2.02%
## [18] target + block + target:block + devices + target:devices + block:devices + target:block:devices + participant : 435628464813 ±2.28%
##
## Against denominator:
## pathlength ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 1.00 8.21e+07
## block 0.74 1.00 1.43e+09
## block:target 0.32 1.00 504.84
## devices 0.74 0.25 0.122
## devices:target 0.32 0.02 0.040
## block:devices 0.32 0.06 0.139
## block:devices:target 0.05 4.80e-04 0.009
##
## * Compared among: all models
## * Priors odds: uniform-equalQuadrant 4:
## Bayes factor analysis
## --------------
## [1] target + participant : 5.186999e+13 ±0.83%
## [2] block + participant : 1.979026 ±1.67%
## [3] target + block + participant : 2.468468e+14 ±2.04%
## [4] target + block + target:block + participant : 7.304235e+13 ±1.59%
## [5] devices + participant : 0.233436 ±0.76%
## [6] target + devices + participant : 1.290134e+13 ±1.14%
## [7] block + devices + participant : 0.4977005 ±5.1%
## [8] target + block + devices + participant : 6.30643e+13 ±2.24%
## [9] target + block + target:block + devices + participant : 2.389808e+13 ±21.61%
## [10] target + devices + target:devices + participant : 2.462306e+12 ±2.17%
## [11] target + block + devices + target:devices + participant : 1.251764e+13 ±3.06%
## [12] target + block + target:block + devices + target:devices + participant : 4.056797e+12 ±9.33%
## [13] block + devices + block:devices + participant : 0.05071406 ±1.4%
## [14] target + block + devices + block:devices + participant : 7.686472e+12 ±1.75%
## [15] target + block + target:block + devices + block:devices + participant : 6.530914e+12 ±64.17%
## [16] target + block + devices + target:devices + block:devices + participant : 1.589891e+12 ±4.51%
## [17] target + block + target:block + devices + target:devices + block:devices + participant : 467813671082 ±2.26%
## [18] target + block + target:block + devices + target:devices + block:devices + target:block:devices + participant : 60338015112 ±3.58%
##
## Against denominator:
## pathlength ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 1.00 4.81e+13
## block 0.74 0.87 2.34
## block:target 0.32 0.21 0.587
## devices 0.74 0.27 0.130
## devices:target 0.32 0.04 0.094
## block:devices 0.32 0.03 0.072
## block:devices:target 0.05 1.19e-04 0.002
##
## * Compared among: all models
## * Priors odds: uniform-equalQuadrant 2:
## Bayes factor analysis
## --------------
## [1] target + participant : 2573.406 ±0.84%
## [2] block + participant : 0.1583539 ±0.86%
## [3] target + block + participant : 445.9088 ±1.13%
## [4] target + block + target:block + participant : 7.911352 ±3.79%
## [5] devices + participant : 0.2794993 ±0.75%
## [6] target + devices + participant : 741.9096 ±1.31%
## [7] block + devices + participant : 0.04471424 ±1.51%
## [8] target + block + devices + participant : 136.9632 ±1.88%
## [9] target + block + target:block + devices + participant : 2.198814 ±1.56%
## [10] target + devices + target:devices + participant : 87.6894 ±2.02%
## [11] target + block + devices + target:devices + participant : 16.18997 ±3.38%
## [12] target + block + target:block + devices + target:devices + participant : 0.2582155 ±1.83%
## [13] block + devices + block:devices + participant : 0.008545412 ±2.19%
## [14] target + block + devices + block:devices + participant : 27.17583 ±2.37%
## [15] target + block + target:block + devices + block:devices + participant : 0.4535525 ±2.18%
## [16] target + block + devices + target:devices + block:devices + participant : 3.07164 ±9.93%
## [17] target + block + target:block + devices + target:devices + block:devices + participant : 0.05230262 ±3.08%
## [18] target + block + target:block + devices + target:devices + block:devices + target:block:devices + participant : 0.008227017 ±29.63%
##
## Against denominator:
## pathlength ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 1.00 968.40
## block 0.74 0.16 0.067
## block:target 0.32 2.69e-03 0.006
## devices 0.74 0.25 0.120
## devices:target 0.32 0.03 0.059
## block:devices 0.32 7.61e-03 0.017
## block:devices:target 0.05 2.03e-06 3.66e-05
##
## * Compared among: all models
## * Priors odds: uniform-equalQuadrant 1A:
## Bayes factor analysis
## --------------
## [1] target + participant : 28308.94 ±0.68%
## [2] block + participant : 12.09498 ±0.65%
## [3] target + block + participant : 567105.5 ±1.17%
## [4] target + block + target:block + participant : 176062.2 ±2.71%
## [5] devices + participant : 0.3284904 ±2.04%
## [6] target + devices + participant : 9913.373 ±2.57%
## [7] block + devices + participant : 4.070521 ±1.28%
## [8] target + block + devices + participant : 187680.7 ±1.57%
## [9] target + block + target:block + devices + participant : 62176.72 ±3.86%
## [10] target + devices + target:devices + participant : 1945.102 ±1.3%
## [11] target + block + devices + target:devices + participant : 39767.48 ±1.79%
## [12] target + block + target:block + devices + target:devices + participant : 12757.44 ±2.78%
## [13] block + devices + block:devices + participant : 0.3071446 ±1.85%
## [14] target + block + devices + block:devices + participant : 15255.01 ±2.66%
## [15] target + block + target:block + devices + block:devices + participant : 4365.143 ±1.69%
## [16] target + block + devices + target:devices + block:devices + participant : 3296.73 ±6.41%
## [17] target + block + target:block + devices + target:devices + block:devices + participant : 999.8198 ±3.77%
## [18] target + block + target:block + devices + target:devices + block:devices + target:block:devices + participant : 265.821 ±16.07%
##
## Against denominator:
## pathlength ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 1.00 2.23e+04
## block 0.74 0.96 9.51
## block:target 0.32 0.23 0.652
## devices 0.74 0.30 0.157
## devices:target 0.32 0.05 0.122
## block:devices 0.32 0.02 0.048
## block:devices:target 0.05 2.39e-04 0.004
##
## * Compared among: all models
## * Priors odds: uniform-equalQuadrant 1L:
## Bayes factor analysis
## --------------
## [1] target + participant : 48585.52 ±0.65%
## [2] block + participant : 74.38372 ±1.13%
## [3] target + block + participant : 7032296 ±2.45%
## [4] target + block + target:block + participant : 6084353 ±1.57%
## [5] devices + participant : 1.10106 ±1.27%
## [6] target + devices + participant : 55545.59 ±1.95%
## [7] block + devices + participant : 80.66824 ±1.43%
## [8] target + block + devices + participant : 7973800 ±3.02%
## [9] target + block + target:block + devices + participant : 7048632 ±1.7%
## [10] target + devices + target:devices + participant : 4862.088 ±2.47%
## [11] target + block + devices + target:devices + participant : 701141 ±2.04%
## [12] target + block + target:block + devices + target:devices + participant : 613142.7 ±1.78%
## [13] block + devices + block:devices + participant : 6.25 ±1.81%
## [14] target + block + devices + block:devices + participant : 601860.2 ±2.22%
## [15] target + block + target:block + devices + block:devices + participant : 528426 ±1.79%
## [16] target + block + devices + target:devices + block:devices + participant : 57378.29 ±4.46%
## [17] target + block + target:block + devices + target:devices + block:devices + participant : 53815.01 ±7.66%
## [18] target + block + target:block + devices + target:devices + block:devices + target:block:devices + participant : 12399.94 ±6.97%
##
## Against denominator:
## pathlength ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 1.00 6.74e+04
## block 0.74 1.00 100.62
## block:target 0.32 0.47 1.89
## devices 0.74 0.57 0.479
## devices:target 0.32 0.05 0.106
## block:devices 0.32 0.04 0.092
## block:devices:target 0.05 4.02e-04 0.007
##
## * Compared among: all models
## * Priors odds: uniform-equalQuadrant 1W:
## Bayes factor analysis
## --------------
## [1] target + participant : 8.297328 ±2.47%
## [2] block + participant : 2.055768e+13 ±0.57%
## [3] target + block + participant : 5.288355e+14 ±2.72%
## [4] target + block + target:block + participant : 3.532875e+15 ±1.8%
## [5] devices + participant : 0.3004535 ±1.03%
## [6] target + devices + participant : 2.446081 ±1.21%
## [7] block + devices + participant : 6.721366e+12 ±2.33%
## [8] target + block + devices + participant : 1.781285e+14 ±4.57%
## [9] target + block + target:block + devices + participant : 1.157241e+15 ±1.64%
## [10] target + devices + target:devices + participant : 0.3378849 ±1.65%
## [11] target + block + devices + target:devices + participant : 2.76792e+13 ±4.83%
## [12] target + block + target:block + devices + target:devices + participant : 1.969823e+14 ±3.19%
## [13] block + devices + block:devices + participant : 1.116372e+12 ±1.5%
## [14] target + block + devices + block:devices + participant : 2.963354e+13 ±6.77%
## [15] target + block + target:block + devices + block:devices + participant : 2.137432e+14 ±3.05%
## [16] target + block + devices + target:devices + block:devices + participant : 4.521609e+12 ±2.28%
## [17] target + block + target:block + devices + target:devices + block:devices + participant : 3.465883e+13 ±3.11%
## [18] target + block + target:block + devices + target:devices + block:devices + target:block:devices + participant : 4.341248e+12 ±2.12%
##
## Against denominator:
## pathlength ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 1.00 74.32
## block 0.74 1.00 1.71e+14
## block:target 0.32 0.87 13.97
## devices 0.74 0.31 0.162
## devices:target 0.32 0.05 0.103
## block:devices 0.32 0.05 0.110
## block:devices:target 0.05 7.31e-04 0.013
##
## * Compared among: all models
## * Priors odds: uniform-equalWe do not find any device effects for path length in reaches to all quadrants.
Sex: Males vs. females
In session 2 the sample for males (N = 11) was smaller than the sample for females (N = 36). One participant identified as neither and was excluded from the comparisons below.
Learning
plotSexCtrlGen()
We conduct the same 3x3x2 mixed design ANOVA as in previous sections, but now we are testing for an effect of sex.
sexLearningGenANOVA()## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Quadrant 1:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 sex 1 45 0.7327354 0.3965332 0.0018597270
## 3 block 2 90 0.4631174 0.6308100 0.0024133324
## 5 target 2 90 0.1638843 0.8490930 0.0007099319
## 4 sex:block 2 90 0.4646060 0.6298813 0.0024210709
## 6 sex:target 2 90 0.6410423 0.5291310 0.0027712090
## 7 block:target 4 180 0.1789585 0.9490442 0.0018079248
## 8 sex:block:target 4 180 0.4662077 0.7604782 0.0046962273
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.995674675 9.090424e-01
## 4 sex:block 0.995674675 9.090424e-01
## 5 target 0.092146331 1.653930e-23 *
## 6 sex:target 0.092146331 1.653930e-23 *
## 7 block:target 0.003236548 2.811784e-48 *
## 8 sex:block:target 0.003236548 2.811784e-48 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF] p[HF]<.05
## 3 block 0.9956933 0.6299823 1.0416958 0.6308100
## 4 sex:block 0.9956933 0.6290549 1.0416958 0.6298813
## 5 target 0.5241492 0.6994195 0.5258241 0.7002216
## 6 sex:target 0.5241492 0.4343754 0.5258241 0.4348381
## 7 block:target 0.5099576 0.8405031 0.5344031 0.8499864
## 8 sex:block:target 0.5099576 0.6326529 0.5344031 0.6416070## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Quadrant 4:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 sex 1 45 0.3560356 0.55370648 0.0009720123
## 3 block 2 90 0.7621760 0.46963787 0.0039016884
## 5 target 2 90 4.0360449 0.02095891 * 0.0164441352
## 4 sex:block 2 90 1.1484789 0.32172184 0.0058676251
## 6 sex:target 2 90 0.5184609 0.59720376 0.0021430893
## 7 block:target 4 180 0.9787513 0.42047813 0.0098920992
## 8 sex:block:target 4 180 1.2714806 0.28290190 0.0128127650
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.765527656 2.799880e-03 *
## 4 sex:block 0.765527656 2.799880e-03 *
## 5 target 0.100932219 1.226468e-22 *
## 6 sex:target 0.100932219 1.226468e-22 *
## 7 block:target 0.002085234 2.768933e-52 *
## 8 sex:block:target 0.002085234 2.768933e-52 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 block 0.8100627 0.44483122 0.8359380 0.44854442
## 4 sex:block 0.8100627 0.31384584 0.8359380 0.31513007
## 5 target 0.5265741 0.04829586 * 0.5284204 0.04814184
## 6 sex:target 0.5265741 0.48415018 0.5284204 0.48475489
## 7 block:target 0.4257628 0.36872163 0.4407953 0.37115412
## 8 sex:block:target 0.4257628 0.28270338 0.4407953 0.28338849
## p[HF]<.05
## 3
## 4
## 5 *
## 6
## 7
## 8## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Quadrant 2:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 sex 1 45 0.03439144 0.8537100 0.0001187453
## 3 block 2 90 1.72698125 0.1836604 0.0072566043
## 5 target 2 90 0.70240387 0.4980881 0.0038914176
## 4 sex:block 2 90 0.77310214 0.4646196 0.0032615714
## 6 sex:target 2 90 0.06968755 0.9327355 0.0003874371
## 7 block:target 4 180 1.18114464 0.3206741 0.0104891744
## 8 sex:block:target 4 180 1.12692679 0.3453068 0.0100125127
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.959969661 4.070663e-01
## 4 sex:block 0.959969661 4.070663e-01
## 5 target 0.058653110 7.987354e-28 *
## 6 sex:target 0.058653110 7.987354e-28 *
## 7 block:target 0.009337512 1.169884e-38 *
## 8 sex:block:target 0.009337512 1.169884e-38 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF] p[HF]<.05
## 3 block 0.9615104 0.1850524 1.0035402 0.1836604
## 4 sex:block 0.9615104 0.4601151 1.0035402 0.4646196
## 5 target 0.5151063 0.4103382 0.5161474 0.4106049
## 6 sex:target 0.5151063 0.8004098 0.5161474 0.8009091
## 7 block:target 0.4942466 0.3113168 0.5168244 0.3125299
## 8 sex:block:target 0.4942466 0.3281233 0.5168244 0.3297665## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Quadrant 1A:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 sex 1 45 0.1195958 0.7310849 0.000377590
## 3 block 2 90 1.7307175 0.1830008 0.008143596
## 5 target 2 90 1.0962126 0.3385534 0.005743971
## 4 sex:block 2 90 1.8929920 0.1565690 0.008900355
## 6 sex:target 2 90 0.4846917 0.6174853 0.002547868
## 7 block:target 4 180 0.9412008 0.4413875 0.008445689
## 8 sex:block:target 4 180 1.8778402 0.1162237 0.016710004
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.939173273 2.514235e-01
## 4 sex:block 0.939173273 2.514235e-01
## 5 target 0.057886873 5.980836e-28 *
## 6 sex:target 0.057886873 5.980836e-28 *
## 7 block:target 0.002598048 2.800456e-50 *
## 8 sex:block:target 0.002598048 2.800456e-50 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF] p[HF]<.05
## 3 block 0.9426610 0.1850780 0.9825519 0.1836403
## 4 sex:block 0.9426610 0.1592259 0.9825519 0.1573800
## 5 target 0.5149031 0.3026071 0.5159300 0.3027362
## 6 sex:target 0.5149031 0.4951778 0.5159300 0.4955373
## 7 block:target 0.4834970 0.3914421 0.5048265 0.3946830
## 8 sex:block:target 0.4834970 0.1603691 0.5048265 0.1584204## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Quadrant 1L:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 sex 1 45 0.7947679 0.3774045 0.0030117592
## 3 block 2 90 0.6778672 0.5102715 0.0028072788
## 5 target 2 90 0.7089492 0.4948886 0.0040211170
## 4 sex:block 2 90 0.1270986 0.8808047 0.0005275617
## 6 sex:target 2 90 1.7011574 0.1882865 0.0095948651
## 7 block:target 4 180 0.4407418 0.7790432 0.0037644552
## 8 sex:block:target 4 180 0.2593759 0.9036320 0.0022188131
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.923415300 1.732748e-01
## 4 sex:block 0.923415300 1.732748e-01
## 5 target 0.069360309 3.194791e-26 *
## 6 sex:target 0.069360309 3.194791e-26 *
## 7 block:target 0.001734237 5.757921e-54 *
## 8 sex:block:target 0.001734237 5.757921e-54 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF] p[HF]<.05
## 3 block 0.9288633 0.5000307 0.9672117 0.5056424
## 4 sex:block 0.9288633 0.8666006 0.9672117 0.8744831
## 5 target 0.5179630 0.4088609 0.5192035 0.4091737
## 6 sex:target 0.5179630 0.1988807 0.5192035 0.1988859
## 7 block:target 0.4597179 0.6284363 0.4783708 0.6362502
## 8 sex:block:target 0.4597179 0.7536441 0.4783708 0.7624327sexLearningGenBayesANOVA()## Quadrant 1:
## Bayes factor analysis
## --------------
## [1] target + participant : 0.06136602 ±0.83%
## [2] block + participant : 0.0376211 ±1.58%
## [3] target + block + participant : 0.00227652 ±0.98%
## [4] target + block + target:block + participant : 2.728012e-05 ±1.61%
## [5] sex + participant : 0.2103828 ±2.39%
## [6] target + sex + participant : 0.01246731 ±1.41%
## [7] block + sex + participant : 0.007778031 ±1.5%
## [8] target + block + sex + participant : 0.000490194 ±2.39%
## [9] target + block + target:block + sex + participant : 5.607912e-06 ±2.11%
## [10] target + sex + target:sex + participant : 0.00143019 ±1.81%
## [11] target + block + sex + target:sex + participant : 5.269761e-05 ±1.78%
## [12] target + block + target:block + sex + target:sex + participant : 4.108723e-07 ±42.67%
## [13] block + sex + block:sex + participant : 0.0007465098 ±2.15%
## [14] target + block + sex + block:sex + participant : 4.657317e-05 ±2.2%
## [15] target + block + target:block + sex + block:sex + participant : 5.8347e-07 ±4.44%
## [16] target + block + sex + target:sex + block:sex + participant : 5.181962e-06 ±3.43%
## [17] target + block + target:block + sex + target:sex + block:sex + participant : 6.602125e-08 ±8.81%
## [18] target + block + target:block + sex + target:sex + block:sex + target:block:sex + participant : 4.867513e-09 ±3.43%
##
## Against denominator:
## percentcomp ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 0.06 0.022
## block 0.74 0.04 0.014
## block:target 0.32 2.54e-05 5.51e-05
## sex 0.74 0.17 0.076
## sex:target 0.32 1.12e-03 0.002
## block:sex 0.32 5.99e-04 0.001
## block:sex:target 0.05 3.65e-09 6.56e-08
##
## * Compared among: all models
## * Priors odds: uniform-equalQuadrant 4:
## Bayes factor analysis
## --------------
## [1] target + participant : 18.53885 ±1%
## [2] block + participant : 0.07461315 ±0.68%
## [3] target + block + participant : 1.456353 ±1.7%
## [4] target + block + target:block + participant : 0.08542796 ±1.33%
## [5] sex + participant : 0.1838123 ±0.82%
## [6] target + sex + participant : 3.393078 ±1.29%
## [7] block + sex + participant : 0.01397605 ±1.53%
## [8] target + block + sex + participant : 0.2729424 ±1.85%
## [9] target + block + target:block + sex + participant : 0.01554888 ±1.42%
## [10] target + sex + target:sex + participant : 0.3715705 ±4.66%
## [11] target + block + sex + target:sex + participant : 0.02891247 ±2.24%
## [12] target + block + target:block + sex + target:sex + participant : 0.001780669 ±3.56%
## [13] block + sex + block:sex + participant : 0.002521849 ±1.71%
## [14] target + block + sex + block:sex + participant : 0.05046361 ±1.8%
## [15] target + block + target:block + sex + block:sex + participant : 0.003024506 ±2.2%
## [16] target + block + sex + target:sex + block:sex + participant : 0.005397293 ±2.73%
## [17] target + block + target:block + sex + target:sex + block:sex + participant : 0.0003879003 ±13.98%
## [18] target + block + target:block + sex + target:sex + block:sex + target:block:sex + participant : 8.734512e-05 ±2.89%
##
## Against denominator:
## percentcomp ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 0.95 6.79
## block 0.74 0.08 0.031
## block:target 0.32 4.17e-03 0.009
## sex 0.74 0.17 0.073
## sex:target 0.32 0.02 0.035
## block:sex 0.32 2.43e-03 0.005
## block:sex:target 0.05 3.43e-06 6.17e-05
##
## * Compared among: all models
## * Priors odds: uniform-equalQuadrant 2:
## Bayes factor analysis
## --------------
## [1] target + participant : 0.1216441 ±0.98%
## [2] block + participant : 0.06214102 ±0.69%
## [3] target + block + participant : 0.008400605 ±5.98%
## [4] target + block + target:block + participant : 0.0001708142 ±3.1%
## [5] sex + participant : 0.1826089 ±2.13%
## [6] target + sex + participant : 0.0217734 ±1.28%
## [7] block + sex + participant : 0.01145028 ±1.51%
## [8] target + block + sex + participant : 0.001386099 ±1.74%
## [9] target + block + target:block + sex + participant : 4.570319e-05 ±32.36%
## [10] target + sex + target:sex + participant : 0.001537007 ±1.5%
## [11] target + block + sex + target:sex + participant : 0.0001061437 ±11.68%
## [12] target + block + target:block + sex + target:sex + participant : 2.07929e-06 ±4.33%
## [13] block + sex + block:sex + participant : 0.001205789 ±1.46%
## [14] target + block + sex + block:sex + participant : 0.0001679793 ±8.03%
## [15] target + block + target:block + sex + block:sex + participant : 3.303042e-06 ±3.5%
## [16] target + block + sex + target:sex + block:sex + participant : 1.073762e-05 ±2.5%
## [17] target + block + target:block + sex + target:sex + block:sex + participant : 2.331033e-07 ±3.09%
## [18] target + block + target:block + sex + target:sex + block:sex + target:block:sex + participant : 3.151934e-08 ±2.23%
##
## Against denominator:
## percentcomp ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 0.11 0.044
## block 0.74 0.06 0.023
## block:target 0.32 1.57e-04 3.41e-04
## sex 0.74 0.16 0.066
## sex:target 0.32 1.17e-03 0.003
## block:sex 0.32 9.83e-04 0.002
## block:sex:target 0.05 2.23e-08 4.02e-07
##
## * Compared among: all models
## * Priors odds: uniform-equalQuadrant 1A:
## Bayes factor analysis
## --------------
## [1] target + participant : 0.3795856 ±0.74%
## [2] block + participant : 0.09167214 ±0.75%
## [3] target + block + participant : 0.03506015 ±1.36%
## [4] target + block + target:block + participant : 0.001265611 ±1.65%
## [5] sex + participant : 0.1849406 ±2.04%
## [6] target + sex + participant : 0.06851548 ±1.15%
## [7] block + sex + participant : 0.01634006 ±1.22%
## [8] target + block + sex + participant : 0.00647635 ±2.04%
## [9] target + block + target:block + sex + participant : 0.0002313429 ±3.28%
## [10] target + sex + target:sex + participant : 0.007465297 ±1.6%
## [11] target + block + sex + target:sex + participant : 0.000745896 ±4.41%
## [12] target + block + target:block + sex + target:sex + participant : 2.45715e-05 ±2.98%
## [13] block + sex + block:sex + participant : 0.005212411 ±1.9%
## [14] target + block + sex + block:sex + participant : 0.002082733 ±2.06%
## [15] target + block + target:block + sex + block:sex + participant : 7.592022e-05 ±3.07%
## [16] target + block + sex + target:sex + block:sex + participant : 0.0002719159 ±18.03%
## [17] target + block + target:block + sex + target:sex + block:sex + participant : 8.074018e-06 ±3.13%
## [18] target + block + target:block + sex + target:sex + block:sex + target:block:sex + participant : 3.745859e-06 ±3.5%
##
## Against denominator:
## percentcomp ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 0.28 0.138
## block 0.74 0.09 0.035
## block:target 0.32 8.94e-04 0.002
## sex 0.74 0.16 0.069
## sex:target 0.32 4.73e-03 0.010
## block:sex 0.32 4.25e-03 0.009
## block:sex:target 0.05 2.08e-06 3.75e-05
##
## * Compared among: all models
## * Priors odds: uniform-equalQuadrant 1L:
## Bayes factor analysis
## --------------
## [1] target + participant : 0.02960601 ±0.9%
## [2] block + participant : 0.08954031 ±0.62%
## [3] target + block + participant : 0.002679146 ±1.32%
## [4] target + block + target:block + participant : 0.0001095324 ±3.15%
## [5] sex + participant : 0.2499192 ±2.33%
## [6] target + sex + participant : 0.006981946 ±1.69%
## [7] block + sex + participant : 0.02192811 ±1.79%
## [8] target + block + sex + participant : 0.0006561675 ±3.02%
## [9] target + block + target:block + sex + participant : 3.280721e-05 ±22.61%
## [10] target + sex + target:sex + participant : 0.002696767 ±1.82%
## [11] target + block + sex + target:sex + participant : 0.0002524664 ±2.02%
## [12] target + block + target:block + sex + target:sex + participant : 1.033742e-05 ±2.44%
## [13] block + sex + block:sex + participant : 0.001606735 ±1.76%
## [14] target + block + sex + block:sex + participant : 5.228517e-05 ±6.59%
## [15] target + block + target:block + sex + block:sex + participant : 1.82826e-06 ±2.53%
## [16] target + block + sex + target:sex + block:sex + participant : 1.944551e-05 ±5.83%
## [17] target + block + target:block + sex + target:sex + block:sex + participant : 8.348463e-07 ±6.3%
## [18] target + block + target:block + sex + target:sex + block:sex + target:block:sex + participant : 5.01473e-08 ±5.44%
##
## Against denominator:
## percentcomp ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 0.03 0.011
## block 0.74 0.08 0.032
## block:target 0.32 1.11e-04 2.39e-04
## sex 0.74 0.20 0.090
## sex:target 0.32 2.12e-03 0.005
## block:sex 0.32 1.20e-03 0.003
## block:sex:target 0.05 3.57e-08 6.42e-07
##
## * Compared among: all models
## * Priors odds: uniform-equalWe do not find any sex effects. We then test washout trials.
sexWashoutLearningANOVA()## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Quadrant 1W:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 sex 1 45 0.1253640 7.249418e-01 0.0005039222
## 3 block 2 90 15.2002255 2.054224e-06 * 0.0437342442
## 5 target 2 90 5.4868713 5.643292e-03 * 0.0265680918
## 4 sex:block 2 90 2.5425953 8.430110e-02 0.0075920745
## 6 sex:target 2 90 2.9671860 5.650310e-02 0.0145449290
## 7 block:target 4 180 1.6545768 1.625712e-01 0.0166245041
## 8 sex:block:target 4 180 0.9797533 4.199305e-01 0.0099113587
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.8619896 0.03811050 *
## 4 sex:block 0.8619896 0.03811050 *
## 5 target 0.8284961 0.01593639 *
## 6 sex:target 0.8284961 0.01593639 *
## 7 block:target 0.7181735 0.10991735
## 8 sex:block:target 0.7181735 0.10991735
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 block 0.8787266 6.934488e-06 * 0.9116351 4.982749e-06
## 4 sex:block 0.8787266 9.185405e-02 0.9116351 8.975061e-02
## 5 target 0.8536036 8.571178e-03 * 0.8838831 7.859984e-03
## 6 sex:target 0.8536036 6.539613e-02 0.8838831 6.345410e-02
## 7 block:target 0.8579514 1.722555e-01 0.9373937 1.667886e-01
## 8 sex:block:target 0.8579514 4.118549e-01 0.9373937 4.165791e-01
## p[HF]<.05
## 3 *
## 4
## 5 *
## 6
## 7
## 8sexWashoutLearningBayesANOVA()## Quadrant 1W:
## Bayes factor analysis
## --------------
## [1] target + participant : 1.223682 ±1.24%
## [2] block + participant : 363.1864 ±0.75%
## [3] target + block + participant : 530.1403 ±1.6%
## [4] target + block + target:block + participant : 34.81543 ±3.81%
## [5] sex + participant : 0.190357 ±1.41%
## [6] target + sex + participant : 0.2314949 ±1.55%
## [7] block + sex + participant : 70.15349 ±1.18%
## [8] target + block + sex + participant : 98.64397 ±1.39%
## [9] target + block + target:block + sex + participant : 6.374445 ±1.55%
## [10] target + sex + target:sex + participant : 0.1816872 ±1.27%
## [11] target + block + sex + target:sex + participant : 95.88229 ±2.17%
## [12] target + block + target:block + sex + target:sex + participant : 5.774597 ±1.64%
## [13] block + sex + block:sex + participant : 16.65058 ±1.64%
## [14] target + block + sex + block:sex + participant : 29.86378 ±11.39%
## [15] target + block + target:block + sex + block:sex + participant : 1.606671 ±2.65%
## [16] target + block + sex + target:sex + block:sex + participant : 25.15601 ±4.74%
## [17] target + block + target:block + sex + target:sex + block:sex + participant : 1.51389 ±3.52%
## [18] target + block + target:block + sex + target:sex + block:sex + target:block:sex + participant : 0.1965825 ±2.51%
##
## Against denominator:
## angdev ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 0.65 0.658
## block 0.74 1.00 161.69
## block:target 0.32 0.04 0.088
## sex 0.74 0.27 0.135
## sex:target 0.32 0.10 0.242
## block:sex 0.32 0.06 0.135
## block:sex:target 0.05 1.53e-04 0.003
##
## * Compared among: all models
## * Priors odds: uniform-equalWe also do not find any effect of sex.
Completion time
plotSexCtrlGenMT()
Next we repeat the same tests but now have completion time as the dependent variable.
sexGenmovementtimeANOVA()## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Quadrant 1:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 sex 1 45 3.1625582 8.210173e-02 0.033052047
## 3 block 2 90 17.6669705 3.371488e-07 * 0.051245239
## 5 target 2 90 13.7237043 6.279979e-06 * 0.051407984
## 4 sex:block 2 90 1.1284253 3.280763e-01 0.003438069
## 6 sex:target 2 90 0.5599547 5.732121e-01 0.002206345
## 7 block:target 4 180 5.9836035 1.525590e-04 * 0.025696274
## 8 sex:block:target 4 180 0.4518930 7.709246e-01 0.001987854
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.8781263 0.0573130231
## 4 sex:block 0.8781263 0.0573130231
## 5 target 0.9662090 0.4694219302
## 6 sex:target 0.9662090 0.4694219302
## 7 block:target 0.4751952 0.0001785472 *
## 8 sex:block:target 0.4751952 0.0001785472 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 block 0.8913659 1.206476e-06 * 0.9256215 8.068004e-07
## 4 sex:block 0.8913659 3.235836e-01 0.9256215 3.251112e-01
## 5 target 0.9673135 8.420703e-06 * 1.0100091 6.279979e-06
## 6 sex:target 0.9673135 5.676002e-01 1.0100091 5.732121e-01
## 7 block:target 0.7428166 7.699589e-04 * 0.8011082 5.324730e-04
## 8 sex:block:target 0.7428166 7.145272e-01 0.8011082 7.290136e-01
## p[HF]<.05
## 3 *
## 4
## 5 *
## 6
## 7 *
## 8## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Quadrant 4:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 sex 1 45 1.3824551 2.458666e-01 0.014638662
## 3 block 2 90 11.9088667 2.579087e-05 * 0.029229957
## 5 target 2 90 26.9053129 6.923393e-10 * 0.115384637
## 4 sex:block 2 90 0.5671685 5.691427e-01 0.001431961
## 6 sex:target 2 90 0.6175276 5.415452e-01 0.002984789
## 7 block:target 4 180 1.3506508 2.529995e-01 0.005506810
## 8 sex:block:target 4 180 0.2470017 9.111936e-01 0.001011616
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.9565352 0.3762021468
## 4 sex:block 0.9565352 0.3762021468
## 5 target 0.8687653 0.0452745848 *
## 6 sex:target 0.8687653 0.0452745848 *
## 7 block:target 0.4762550 0.0001855554 *
## 8 sex:block:target 0.4762550 0.0001855554 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 block 0.9583457 3.548876e-05 * 1.0000138 2.579087e-05
## 4 sex:block 0.9583457 5.620362e-01 1.0000138 5.691427e-01
## 5 target 0.8839899 5.372273e-09 * 0.9174573 2.973441e-09
## 6 sex:target 0.8839899 5.225551e-01 0.9174573 5.282669e-01
## 7 block:target 0.7104402 2.616754e-01 0.7633205 2.603570e-01
## 8 sex:block:target 0.7104402 8.532926e-01 0.7633205 8.665554e-01
## p[HF]<.05
## 3 *
## 4
## 5 *
## 6
## 7
## 8## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Quadrant 2:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 sex 1 45 3.2042254 0.080178153 0.0171858674
## 3 block 2 90 2.6881593 0.073466259 0.0101508028
## 5 target 2 90 4.9318178 0.009280709 * 0.0247133101
## 4 sex:block 2 90 0.9951759 0.373689017 0.0037820786
## 6 sex:target 2 90 0.1656925 0.847564588 0.0008505992
## 7 block:target 4 180 0.5258492 0.716862342 0.0040911912
## 8 sex:block:target 4 180 0.6571479 0.622573399 0.0051074993
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.396124899 1.420061e-09 *
## 4 sex:block 0.396124899 1.420061e-09 *
## 5 target 0.474439378 7.515814e-08 *
## 6 sex:target 0.474439378 7.515814e-08 *
## 7 block:target 0.003929628 1.639828e-46 *
## 8 sex:block:target 0.003929628 1.639828e-46 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 block 0.6234899 0.09889946 0.6326543 0.09822122
## 4 sex:block 0.6234899 0.34099379 0.6326543 0.34208838
## 5 target 0.6554967 0.02152382 * 0.6672811 0.02091204
## 6 sex:target 0.6554967 0.75292853 0.6672811 0.75721062
## 7 block:target 0.2945556 0.50022125 0.2977870 0.50210299
## 8 sex:block:target 0.2945556 0.44508021 0.2977870 0.44663056
## p[HF]<.05
## 3
## 4
## 5 *
## 6
## 7
## 8## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Quadrant 1A:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 sex 1 45 0.2107667 6.483771e-01 0.002119968
## 3 block 2 90 1.0265326 3.624028e-01 0.003712981
## 5 target 2 90 21.0153926 3.239878e-08 * 0.084215222
## 4 sex:block 2 90 0.9241990 4.005821e-01 0.003344077
## 6 sex:target 2 90 1.5467562 2.185441e-01 0.006722828
## 7 block:target 4 180 0.2844534 8.877923e-01 0.001175167
## 8 sex:block:target 4 180 0.5080282 7.298892e-01 0.002096889
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.8252798 0.01462941 *
## 4 sex:block 0.8252798 0.01462941 *
## 5 target 0.9934583 0.86555016
## 6 sex:target 0.9934583 0.86555016
## 7 block:target 0.7470884 0.17895955
## 8 sex:block:target 0.7470884 0.17895955
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 block 0.8512665 3.529128e-01 0.8813047 3.550193e-01
## 4 sex:block 0.8512665 3.876755e-01 0.8813047 3.904966e-01
## 5 target 0.9935008 3.547370e-08 * 1.0392449 3.239878e-08
## 6 sex:target 0.9935008 2.186817e-01 1.0392449 2.185441e-01
## 7 block:target 0.8682391 8.636458e-01 0.9497184 8.792202e-01
## 8 sex:block:target 0.8682391 7.041622e-01 0.9497184 7.205130e-01
## p[HF]<.05
## 3
## 4
## 5 *
## 6
## 7
## 8## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Quadrant 1L:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 sex 1 45 0.4130008 5.237114e-01 0.002845752
## 3 block 2 90 7.0375631 1.446440e-03 * 0.028863947
## 5 target 2 90 10.2558715 9.717032e-05 * 0.040919348
## 4 sex:block 2 90 1.0827314 3.430390e-01 0.004551900
## 6 sex:target 2 90 0.2978642 7.431312e-01 0.001237603
## 7 block:target 4 180 1.8817598 1.155333e-01 0.012870426
## 8 sex:block:target 4 180 0.2571671 9.049948e-01 0.001778676
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.8340194 1.844486e-02 *
## 4 sex:block 0.8340194 1.844486e-02 *
## 5 target 0.7280056 9.267522e-04 *
## 6 sex:target 0.7280056 9.267522e-04 *
## 7 block:target 0.1644314 3.620330e-13 *
## 8 sex:block:target 0.1644314 3.620330e-13 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 block 0.8576472 0.0025676273 * 0.8883455 0.0022681503
## 4 sex:block 0.8576472 0.3356590916 0.8883455 0.3374190370
## 5 target 0.7861670 0.0003870587 * 0.8097069 0.0003322597
## 6 sex:target 0.7861670 0.6900447188 0.8097069 0.6966358913
## 7 block:target 0.5042889 0.1578713860 0.5280546 0.1556793670
## 8 sex:block:target 0.5042889 0.7756610946 0.5280546 0.7855918382
## p[HF]<.05
## 3 *
## 4
## 5 *
## 6
## 7
## 8## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Quadrant 1W:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 sex 1 45 0.8973162 3.485617e-01 0.0080123253
## 3 block 2 90 52.8052594 6.733854e-16 * 0.1068858738
## 5 target 2 90 4.5196989 1.347576e-02 * 0.0170611070
## 4 sex:block 2 90 0.3869188 6.802704e-01 0.0008761436
## 6 sex:target 2 90 1.4352012 2.434631e-01 0.0054814676
## 7 block:target 4 180 2.9913949 2.016581e-02 * 0.0208377462
## 8 sex:block:target 4 180 1.2202005 3.038514e-01 0.0086059699
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.8819925 6.312876e-02
## 4 sex:block 0.8819925 6.312876e-02
## 5 target 0.7292377 9.618787e-04 *
## 6 sex:target 0.7292377 9.618787e-04 *
## 7 block:target 0.1150371 2.952720e-16 *
## 8 sex:block:target 0.1150371 2.952720e-16 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 block 0.8944484 1.804840e-14 * 0.9290349 6.141505e-15
## 4 sex:block 0.8944484 6.571794e-01 0.9290349 6.650429e-01
## 5 target 0.7869292 2.121207e-02 * 0.8105428 2.016990e-02
## 6 sex:target 0.7869292 2.441048e-01 0.8105428 2.441910e-01
## 7 block:target 0.5108774 5.402493e-02 0.5354339 5.138971e-02
## 8 sex:block:target 0.5108774 3.004504e-01 0.5354339 3.013470e-01
## p[HF]<.05
## 3 *
## 4
## 5 *
## 6
## 7
## 8sexGenmovementtimeBayesANOVA()## Quadrant 1:
## Bayes factor analysis
## --------------
## [1] target + participant : 529988482 ±2.06%
## [2] block + participant : 420905959 ±3.18%
## [3] target + block + participant : 7.485448e+18 ±4.75%
## [4] target + block + target:block + participant : 3.003888e+20 ±1.79%
## [5] sex + participant : 0.9698249 ±1.09%
## [6] target + sex + participant : 503924426 ±0.99%
## [7] block + sex + participant : 415025314 ±1.21%
## [8] target + block + sex + participant : 7.07201e+18 ±1.34%
## [9] target + block + target:block + sex + participant : 3.879984e+20 ±17.74%
## [10] target + sex + target:sex + participant : 66943087 ±2.97%
## [11] target + block + sex + target:sex + participant : 1.06872e+18 ±2.78%
## [12] target + block + target:block + sex + target:sex + participant : 4.585956e+19 ±2.23%
## [13] block + sex + block:sex + participant : 72842242 ±1.63%
## [14] target + block + sex + block:sex + participant : 1.437878e+18 ±1.65%
## [15] target + block + target:block + sex + block:sex + participant : 6.405555e+19 ±1.63%
## [16] target + block + sex + target:sex + block:sex + participant : 2.105329e+17 ±4.38%
## [17] target + block + target:block + sex + target:sex + block:sex + participant : 9.907091e+18 ±3.18%
## [18] target + block + target:block + sex + target:sex + block:sex + target:block:sex + participant : 6.008897e+17 ±4.71%
##
## Against denominator:
## movementtime ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 1.00 3.25e+11
## block 0.74 1.00 2.68e+11
## block:target 0.32 0.98 101.45
## sex 0.74 0.63 0.601
## sex:target 0.32 0.07 0.163
## block:sex 0.32 0.09 0.220
## block:sex:target 0.05 7.27e-04 0.013
##
## * Compared among: all models
## * Priors odds: uniform-equalQuadrant 4:
## Bayes factor analysis
## --------------
## [1] target + participant : 2.341037e+17 ±1.78%
## [2] block + participant : 390.5809 ±1.23%
## [3] target + block + participant : 1.27922e+21 ±1.12%
## [4] target + block + target:block + participant : 1.227503e+20 ±1.21%
## [5] sex + participant : 0.4820891 ±0.86%
## [6] target + sex + participant : 1.178863e+17 ±1.28%
## [7] block + sex + participant : 198.5045 ±3.26%
## [8] target + block + sex + participant : 6.896814e+20 ±1.72%
## [9] target + block + target:block + sex + participant : 6.682027e+19 ±2.59%
## [10] target + sex + target:sex + participant : 1.537795e+16 ±1.57%
## [11] target + block + sex + target:sex + participant : 9.876765e+19 ±6.68%
## [12] target + block + target:block + sex + target:sex + participant : 9.527741e+18 ±3.38%
## [13] block + sex + block:sex + participant : 16.74476 ±2.45%
## [14] target + block + sex + block:sex + participant : 6.565298e+19 ±3.4%
## [15] target + block + target:block + sex + block:sex + participant : 6.536056e+18 ±2.58%
## [16] target + block + sex + target:sex + block:sex + participant : 9.278379e+18 ±4.2%
## [17] target + block + target:block + sex + target:sex + block:sex + participant : 8.868724e+17 ±4.05%
## [18] target + block + target:block + sex + target:sex + block:sex + target:block:sex + participant : 4.94604e+16 ±3.56%
##
## Against denominator:
## movementtime ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 1.00 1.38e+18
## block 0.74 1.00 2.28e+03
## block:target 0.32 0.09 0.209
## sex 0.74 0.40 0.241
## sex:target 0.32 0.05 0.115
## block:sex 0.32 0.04 0.079
## block:sex:target 0.05 2.11e-05 3.79e-04
##
## * Compared among: all models
## * Priors odds: uniform-equalQuadrant 2:
## Bayes factor analysis
## --------------
## [1] target + participant : 203.1009 ±2.5%
## [2] block + participant : 5.354053 ±0.71%
## [3] target + block + participant : 1449.579 ±3.18%
## [4] target + block + target:block + participant : 236.1235 ±7.59%
## [5] sex + participant : 0.6843545 ±0.81%
## [6] target + sex + participant : 142.227 ±1.16%
## [7] block + sex + participant : 3.99391 ±3.94%
## [8] target + block + sex + participant : 1125.935 ±8.06%
## [9] target + block + target:block + sex + participant : 162.1958 ±2.1%
## [10] target + sex + target:sex + participant : 11.61568 ±3.26%
## [11] target + block + sex + target:sex + participant : 80.93573 ±2.28%
## [12] target + block + target:block + sex + target:sex + participant : 13.06536 ±3.02%
## [13] block + sex + block:sex + participant : 0.6098892 ±2.52%
## [14] target + block + sex + block:sex + participant : 160.9404 ±2.12%
## [15] target + block + target:block + sex + block:sex + participant : 25.40485 ±2.44%
## [16] target + block + sex + target:sex + block:sex + participant : 13.30256 ±2.21%
## [17] target + block + target:block + sex + target:sex + block:sex + participant : 2.340088 ±5.66%
## [18] target + block + target:block + sex + target:sex + block:sex + target:block:sex + participant : 0.2944861 ±6.26%
##
## Against denominator:
## movementtime ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 1.00 111.27
## block 0.74 0.90 3.27
## block:target 0.32 0.12 0.298
## sex 0.74 0.48 0.329
## sex:target 0.32 0.03 0.075
## block:sex 0.32 0.06 0.128
## block:sex:target 0.05 8.09e-05 0.001
##
## * Compared among: all models
## * Priors odds: uniform-equalQuadrant 1A:
## Bayes factor analysis
## --------------
## [1] target + participant : 22759886612 ±1.06%
## [2] block + participant : 0.5428501 ±0.69%
## [3] target + block + participant : 20836023951 ±1.7%
## [4] target + block + target:block + participant : 502486907 ±1.57%
## [5] sex + participant : 0.3018191 ±0.76%
## [6] target + sex + participant : 7192714945 ±1.19%
## [7] block + sex + participant : 0.1727942 ±2.87%
## [8] target + block + sex + participant : 6488260587 ±1.53%
## [9] target + block + target:block + sex + participant : 154670349 ±1.32%
## [10] target + sex + target:sex + participant : 2477093269 ±2.23%
## [11] target + block + sex + target:sex + participant : 2239087211 ±1.56%
## [12] target + block + target:block + sex + target:sex + participant : 56557490 ±2.13%
## [13] block + sex + block:sex + participant : 0.02674648 ±1.35%
## [14] target + block + sex + block:sex + participant : 1252055197 ±2.17%
## [15] target + block + target:block + sex + block:sex + participant : 29333666 ±2.32%
## [16] target + block + sex + target:sex + block:sex + participant : 434089226 ±2.12%
## [17] target + block + target:block + sex + target:sex + block:sex + participant : 10704220 ±3.5%
## [18] target + block + target:block + sex + target:sex + block:sex + target:block:sex + participant : 767155.5 ±2.55%
##
## Against denominator:
## movementtime ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 1.00 1.13e+10
## block 0.74 0.50 0.352
## block:target 0.32 0.01 0.026
## sex 0.74 0.32 0.165
## sex:target 0.32 0.08 0.191
## block:sex 0.32 0.03 0.060
## block:sex:target 0.05 1.19e-05 2.14e-04
##
## * Compared among: all models
## * Priors odds: uniform-equalQuadrant 1L:
## Bayes factor analysis
## --------------
## [1] target + participant : 11718.53 ±0.76%
## [2] block + participant : 48.60168 ±0.63%
## [3] target + block + participant : 1017274 ±1.07%
## [4] target + block + target:block + participant : 409159.6 ±1.31%
## [5] sex + participant : 0.2626337 ±0.83%
## [6] target + sex + participant : 3068.32 ±0.97%
## [7] block + sex + participant : 13.76004 ±4.77%
## [8] target + block + sex + participant : 271660.8 ±2.06%
## [9] target + block + target:block + sex + participant : 117291.2 ±3.25%
## [10] target + sex + target:sex + participant : 279.2635 ±4.58%
## [11] target + block + sex + target:sex + participant : 23728.92 ±3.59%
## [12] target + block + target:block + sex + target:sex + participant : 9140.993 ±1.62%
## [13] block + sex + block:sex + participant : 1.994219 ±1.62%
## [14] target + block + sex + block:sex + participant : 44975.18 ±2.17%
## [15] target + block + target:block + sex + block:sex + participant : 19035.56 ±2.54%
## [16] target + block + sex + target:sex + block:sex + participant : 3724.852 ±1.94%
## [17] target + block + target:block + sex + target:sex + block:sex + participant : 1664.676 ±4.03%
## [18] target + block + target:block + sex + target:sex + block:sex + target:block:sex + participant : 94.24416 ±2.33%
##
## Against denominator:
## movementtime ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 1.00 1.05e+04
## block 0.74 0.99 45.46
## block:target 0.32 0.29 0.876
## sex 0.74 0.26 0.123
## sex:target 0.32 0.02 0.044
## block:sex 0.32 0.04 0.081
## block:sex:target 0.05 4.88e-05 8.78e-04
##
## * Compared among: all models
## * Priors odds: uniform-equalQuadrant 1W:
## Bayes factor analysis
## --------------
## [1] target + participant : 3.99808 ±0.92%
## [2] block + participant : 1.164663e+17 ±0.89%
## [3] target + block + participant : 1.77735e+18 ±1.02%
## [4] target + block + target:block + participant : 2.971426e+20 ±1.9%
## [5] sex + participant : 0.3461796 ±0.99%
## [6] target + sex + participant : 1.411639 ±2.37%
## [7] block + sex + participant : 4.504697e+16 ±3.26%
## [8] target + block + sex + participant : 6.715032e+17 ±1.31%
## [9] target + block + target:block + sex + participant : 1.132877e+20 ±1.72%
## [10] target + sex + target:sex + participant : 0.2653025 ±2.26%
## [11] target + block + sex + target:sex + participant : 2.178179e+17 ±20.88%
## [12] target + block + target:block + sex + target:sex + participant : 3.2066e+19 ±5.13%
## [13] block + sex + block:sex + participant : 3.756126e+15 ±1.66%
## [14] target + block + sex + block:sex + participant : 6.323239e+16 ±4.92%
## [15] target + block + target:block + sex + block:sex + participant : 1.018283e+19 ±2.03%
## [16] target + block + sex + target:sex + block:sex + participant : 1.408662e+16 ±1.74%
## [17] target + block + target:block + sex + target:sex + block:sex + participant : 2.748139e+18 ±3.17%
## [18] target + block + target:block + sex + target:sex + block:sex + target:block:sex + participant : 8.928715e+17 ±1.93%
##
## Against denominator:
## movementtime ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 1.00 992.03
## block 0.74 1.00 2.34e+19
## block:target 0.32 0.99 339.84
## sex 0.74 0.35 0.191
## sex:target 0.32 0.08 0.184
## block:sex 0.32 0.03 0.068
## block:sex:target 0.05 1.94e-03 0.035
##
## * Compared among: all models
## * Priors odds: uniform-equalWe find no sex effects for completion time.
Path length
plotSexCtrlGenPL()
Then we conduct tests with path length as the dependent variable.
sexGenpathlengthANOVA()## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Quadrant 1:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 sex 1 45 0.03913817 8.440662e-01 0.0002505818
## 3 block 2 90 21.40299449 2.489535e-08 * 0.0683760248
## 5 target 2 90 11.10292834 4.900205e-05 * 0.0438808645
## 4 sex:block 2 90 0.31396031 7.313449e-01 0.0010754645
## 6 sex:target 2 90 0.58651009 5.583771e-01 0.0024185189
## 7 block:target 4 180 3.73305461 6.057686e-03 * 0.0298964636
## 8 sex:block:target 4 180 0.51100591 7.277112e-01 0.0042008297
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.9894036 7.910741e-01
## 4 sex:block 0.9894036 7.910741e-01
## 5 target 0.9183769 1.536246e-01
## 6 sex:target 0.9183769 1.536246e-01
## 7 block:target 0.3703685 2.088371e-06 *
## 8 sex:block:target 0.3703685 2.088371e-06 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 block 0.9895148 2.889325e-08 * 1.0347902 2.489535e-08
## 4 sex:block 0.9895148 7.290689e-01 1.0347902 7.313449e-01
## 5 target 0.9245365 8.357896e-05 * 0.9624052 6.392440e-05
## 6 sex:target 0.9245365 5.456642e-01 0.9624052 5.521623e-01
## 7 block:target 0.7055986 1.473098e-02 * 0.7576896 1.257088e-02
## 8 sex:block:target 0.7055986 6.642340e-01 0.7576896 6.772237e-01
## p[HF]<.05
## 3 *
## 4
## 5 *
## 6
## 7 *
## 8## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Quadrant 4:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 sex 1 45 0.4893904 4.878000e-01 0.0034564142
## 3 block 2 90 3.4624001 3.559113e-02 * 0.0122484469
## 5 target 2 90 19.3679906 1.010218e-07 * 0.0869632841
## 4 sex:block 2 90 0.1731816 8.412644e-01 0.0006198529
## 6 sex:target 2 90 0.6329142 5.333888e-01 0.0031028324
## 7 block:target 4 180 1.3438030 2.554725e-01 0.0088385182
## 8 sex:block:target 4 180 0.7371760 5.677479e-01 0.0048680084
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.9416379 2.663464e-01
## 4 sex:block 0.9416379 2.663464e-01
## 5 target 0.9004667 9.960662e-02
## 6 sex:target 0.9004667 9.960662e-02
## 7 block:target 0.4141565 1.583312e-05 *
## 8 sex:block:target 0.4141565 1.583312e-05 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 block 0.9448562 3.834300e-02 * 0.9849943 3.631967e-02
## 4 sex:block 0.9448562 8.294261e-01 0.9849943 8.381426e-01
## 5 target 0.9094768 3.241234e-07 * 0.9456911 2.032557e-07
## 6 sex:target 0.9094768 5.191385e-01 0.9456911 5.249958e-01
## 7 block:target 0.6940062 2.641312e-01 0.7442285 2.630089e-01
## 8 sex:block:target 0.6940062 5.219560e-01 0.7442285 5.306512e-01
## p[HF]<.05
## 3 *
## 4
## 5 *
## 6
## 7
## 8## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Quadrant 2:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 sex 1 45 0.06107874 0.805923085 0.0005111974
## 3 block 2 90 0.34340100 0.710279053 0.0012021316
## 5 target 2 90 6.15745139 0.003116468 * 0.0276278785
## 4 sex:block 2 90 1.68829150 0.190635572 0.0058824471
## 6 sex:target 2 90 0.36028515 0.698478751 0.0016597359
## 7 block:target 4 180 0.38891799 0.816398225 0.0022232335
## 8 sex:block:target 4 180 0.94661679 0.438325244 0.0053940988
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.9690089 0.50027749
## 4 sex:block 0.9690089 0.50027749
## 5 target 0.9416220 0.26624700
## 6 sex:target 0.9416220 0.26624700
## 7 block:target 0.6151913 0.01230653 *
## 8 sex:block:target 0.6151913 0.01230653 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 block 0.9699405 0.703774559 1.0129387 0.710279053
## 4 sex:block 0.9699405 0.191637891 1.0129387 0.190635572
## 5 target 0.9448420 0.003750484 * 0.9849784 0.003277545
## 6 sex:target 0.9448420 0.686504095 0.9849784 0.695289172
## 7 block:target 0.8134723 0.777118358 0.8843871 0.793262447
## 8 sex:block:target 0.8134723 0.425379880 0.8843871 0.430701645
## p[HF]<.05
## 3
## 4
## 5 *
## 6
## 7
## 8## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Quadrant 1A:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 sex 1 45 0.3066247 0.5824999997 0.003012967
## 3 block 2 90 9.0069199 0.0002718565 * 0.031904172
## 5 target 2 90 8.7118540 0.0003478617 * 0.037498894
## 4 sex:block 2 90 3.0400969 0.0527702001 0.011001099
## 6 sex:target 2 90 0.8974529 0.4112224442 0.003997411
## 7 block:target 4 180 1.8212825 0.1266267942 0.007654671
## 8 sex:block:target 4 180 0.6496438 0.6278379076 0.002743901
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.8431721 0.02345078 *
## 4 sex:block 0.8431721 0.02345078 *
## 5 target 0.8444511 0.02424596 *
## 6 sex:target 0.8444511 0.02424596 *
## 7 block:target 0.7445814 0.17193504
## 8 sex:block:target 0.7445814 0.17193504
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 block 0.8644328 0.0005745969 * 0.8958376 0.0004829812
## 4 sex:block 0.8644328 0.0608413851 0.8958376 0.0588719270
## 5 target 0.8653896 0.0007098163 * 0.8968944 0.0006005076
## 6 sex:target 0.8653896 0.3988036760 0.8968944 0.4019070230
## 7 block:target 0.8594638 0.1373448259 0.9392040 0.1311604299
## 8 sex:block:target 0.8594638 0.6049205111 0.9392040 0.6183171935
## p[HF]<.05
## 3 *
## 4
## 5 *
## 6
## 7
## 8## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Quadrant 1L:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 sex 1 45 0.01450175 9.046840e-01 0.0001113618
## 3 block 2 90 10.90426278 5.748328e-05 * 0.0292637417
## 5 target 2 90 6.32319061 2.694319e-03 * 0.0290190045
## 4 sex:block 2 90 2.30713107 1.054061e-01 0.0063378696
## 6 sex:target 2 90 0.29339380 7.464389e-01 0.0013847922
## 7 block:target 4 180 2.11958827 8.019614e-02 0.0147253769
## 8 sex:block:target 4 180 0.07914692 9.886186e-01 0.0005577626
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.8327128 0.017819501 *
## 4 sex:block 0.8327128 0.017819501 *
## 5 target 0.8648896 0.041033181 *
## 6 sex:target 0.8648896 0.041033181 *
## 7 block:target 0.5617444 0.002949464 *
## 8 sex:block:target 0.5617444 0.002949464 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 block 0.8566872 0.0001553323 * 0.8872859 0.0001255783
## 4 sex:block 0.8566872 0.1140487902 0.8872859 0.1121681472
## 5 target 0.8809716 0.0040804954 * 0.9141182 0.0036343959
## 6 sex:target 0.8809716 0.7186362254 0.9141182 0.7267956180
## 7 block:target 0.7707451 0.0987743368 0.8338921 0.0932536174
## 8 sex:block:target 0.7707451 0.9733826746 0.8338921 0.9789931352
## p[HF]<.05
## 3 *
## 4
## 5 *
## 6
## 7
## 8## Warning: Data is unbalanced (unequal N per group). Make sure you specified a
## well-considered value for the type argument to ezANOVA().## Quadrant 1W:
## $ANOVA
## Effect DFn DFd F p p<.05 ges
## 2 sex 1 45 0.02091602 8.856538e-01 1.024454e-04
## 3 block 2 90 27.44426792 4.947455e-10 * 1.142891e-01
## 5 target 2 90 6.40864851 2.499970e-03 * 2.854136e-02
## 4 sex:block 2 90 0.02101116 9.792128e-01 9.877984e-05
## 6 sex:target 2 90 0.49089507 6.137075e-01 2.245413e-03
## 7 block:target 4 180 4.45947998 1.846774e-03 * 3.460322e-02
## 8 sex:block:target 4 180 1.17457812 3.235777e-01 9.352495e-03
##
## $`Mauchly's Test for Sphericity`
## Effect W p p<.05
## 3 block 0.22927892 8.472484e-15 *
## 4 sex:block 0.22927892 8.472484e-15 *
## 5 target 0.71255222 5.780526e-04 *
## 6 sex:target 0.71255222 5.780526e-04 *
## 7 block:target 0.03982253 1.283667e-25 *
## 8 sex:block:target 0.03982253 1.283667e-25 *
##
## $`Sphericity Corrections`
## Effect GGe p[GG] p[GG]<.05 HFe p[HF]
## 3 block 0.5647417 1.276467e-06 * 0.5693600 1.173848e-06
## 4 sex:block 0.5647417 9.089931e-01 0.5693600 9.104643e-01
## 5 target 0.7767305 5.533849e-03 * 0.7993641 5.104058e-03
## 6 sex:target 0.7767305 5.670258e-01 0.7993641 5.723080e-01
## 7 block:target 0.4682228 1.624627e-02 * 0.4878196 1.497372e-02
## 8 sex:block:target 0.4682228 3.116649e-01 0.4878196 3.129187e-01
## p[HF]<.05
## 3 *
## 4
## 5 *
## 6
## 7 *
## 8sexGenpathlengthBayesANOVA()## Quadrant 1:
## Bayes factor analysis
## --------------
## [1] target + participant : 255213.2 ±1.77%
## [2] block + participant : 1903652 ±4.28%
## [3] target + block + participant : 2.595398e+12 ±2.78%
## [4] target + block + target:block + participant : 7.119459e+14 ±2.91%
## [5] sex + participant : 0.2086014 ±0.85%
## [6] target + sex + participant : 54911.18 ±1.75%
## [7] block + sex + participant : 397832.2 ±1.95%
## [8] target + block + sex + participant : 566384447002 ±1.74%
## [9] target + block + target:block + sex + participant : 1.57114e+14 ±3.5%
## [10] target + sex + target:sex + participant : 6452.745 ±4.26%
## [11] target + block + sex + target:sex + participant : 70292448468 ±2.39%
## [12] target + block + target:block + sex + target:sex + participant : 2.014151e+13 ±2.38%
## [13] block + sex + block:sex + participant : 29083.84 ±2.78%
## [14] target + block + sex + block:sex + participant : 41859731729 ±2.13%
## [15] target + block + target:block + sex + block:sex + participant : 1.182861e+13 ±3.81%
## [16] target + block + sex + target:sex + block:sex + participant : 5023921697 ±3.04%
## [17] target + block + target:block + sex + target:sex + block:sex + participant : 1.488972e+12 ±3.34%
## [18] target + block + target:block + sex + target:sex + block:sex + target:block:sex + participant : 156567582042 ±2.59%
##
## Against denominator:
## pathlength ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 1.00 1.39e+08
## block 0.74 1.00 1.02e+09
## block:target 0.32 1.00 596.47
## sex 0.74 0.21 0.096
## sex:target 0.32 0.02 0.054
## block:sex 0.32 0.01 0.033
## block:sex:target 0.05 1.73e-04 0.003
##
## * Compared among: all models
## * Priors odds: uniform-equalQuadrant 4:
## Bayes factor analysis
## --------------
## [1] target + participant : 6.491249e+13 ±1.86%
## [2] block + participant : 1.98631 ±0.74%
## [3] target + block + participant : 3.119025e+14 ±1.11%
## [4] target + block + target:block + participant : 9.297536e+13 ±1.6%
## [5] sex + participant : 0.2608503 ±0.92%
## [6] target + sex + participant : 1.886722e+13 ±2.63%
## [7] block + sex + participant : 0.5351429 ±2.17%
## [8] target + block + sex + participant : 9.368587e+13 ±3.04%
## [9] target + block + target:block + sex + participant : 2.610399e+13 ±1.51%
## [10] target + sex + target:sex + participant : 2.681891e+12 ±1.48%
## [11] target + block + sex + target:sex + participant : 1.383632e+13 ±1.9%
## [12] target + block + target:block + sex + target:sex + participant : 4.148902e+12 ±3.63%
## [13] block + sex + block:sex + participant : 0.03852805 ±1.48%
## [14] target + block + sex + block:sex + participant : 7.354672e+12 ±4.81%
## [15] target + block + target:block + sex + block:sex + participant : 2.137652e+12 ±2.34%
## [16] target + block + sex + target:sex + block:sex + participant : 1.046274e+12 ±2.23%
## [17] target + block + target:block + sex + target:sex + block:sex + participant : 340842118896 ±3.63%
## [18] target + block + target:block + sex + target:sex + block:sex + target:block:sex + participant : 36213698039 ±3.26%
##
## Against denominator:
## pathlength ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 1.00 5.98e+13
## block 0.74 0.86 2.29
## block:target 0.32 0.20 0.530
## sex 0.74 0.27 0.129
## sex:target 0.32 0.03 0.077
## block:sex 0.32 0.02 0.038
## block:sex:target 0.05 5.66e-05 0.001
##
## * Compared among: all models
## * Priors odds: uniform-equalQuadrant 2:
## Bayes factor analysis
## --------------
## [1] target + participant : 1021.276 ±0.99%
## [2] block + participant : 0.2010523 ±0.8%
## [3] target + block + participant : 230.2265 ±1.16%
## [4] target + block + target:block + participant : 4.343028 ±7.83%
## [5] sex + participant : 0.2611768 ±1.59%
## [6] target + sex + participant : 266.8834 ±1.11%
## [7] block + sex + participant : 0.05378105 ±1.3%
## [8] target + block + sex + participant : 64.3264 ±2.62%
## [9] target + block + target:block + sex + participant : 1.066884 ±1.98%
## [10] target + sex + target:sex + participant : 26.90982 ±1.94%
## [11] target + block + sex + target:sex + participant : 6.050591 ±2.01%
## [12] target + block + target:block + sex + target:sex + participant : 0.1034597 ±2.21%
## [13] block + sex + block:sex + participant : 0.01496894 ±1.32%
## [14] target + block + sex + block:sex + participant : 19.68001 ±2.33%
## [15] target + block + target:block + sex + block:sex + participant : 0.3667472 ±7.75%
## [16] target + block + sex + target:sex + block:sex + participant : 2.070573 ±7.56%
## [17] target + block + target:block + sex + target:sex + block:sex + participant : 0.03286447 ±4.16%
## [18] target + block + target:block + sex + target:sex + block:sex + target:block:sex + participant : 0.003727339 ±3.79%
##
## Against denominator:
## pathlength ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 1.00 383.35
## block 0.74 0.20 0.089
## block:target 0.32 3.60e-03 0.008
## sex 0.74 0.24 0.110
## sex:target 0.32 0.02 0.047
## block:sex 0.32 0.01 0.030
## block:sex:target 0.05 2.27e-06 4.08e-05
##
## * Compared among: all models
## * Priors odds: uniform-equalQuadrant 1A:
## Bayes factor analysis
## --------------
## [1] target + participant : 49649 ±0.68%
## [2] block + participant : 10.54841 ±5.89%
## [3] target + block + participant : 829120.8 ±1.29%
## [4] target + block + target:block + participant : 234805.4 ±2.09%
## [5] sex + participant : 0.3158455 ±1.24%
## [6] target + sex + participant : 16223.06 ±1.17%
## [7] block + sex + participant : 3.192355 ±1.57%
## [8] target + block + sex + participant : 271480.8 ±2.1%
## [9] target + block + target:block + sex + participant : 82868.61 ±7.97%
## [10] target + sex + target:sex + participant : 2888.964 ±2.14%
## [11] target + block + sex + target:sex + participant : 50212.57 ±1.96%
## [12] target + block + target:block + sex + target:sex + participant : 15037.53 ±5.71%
## [13] block + sex + block:sex + participant : 2.488065 ±1.15%
## [14] target + block + sex + block:sex + participant : 263818.3 ±1.71%
## [15] target + block + target:block + sex + block:sex + participant : 80875.09 ±2.45%
## [16] target + block + sex + target:sex + block:sex + participant : 51645.37 ±3.45%
## [17] target + block + target:block + sex + target:sex + block:sex + participant : 16533.84 ±3.74%
## [18] target + block + target:block + sex + target:sex + block:sex + target:block:sex + participant : 1400.921 ±3.82%
##
## Against denominator:
## pathlength ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 1.00 4.00e+04
## block 0.74 0.97 9.86
## block:target 0.32 0.22 0.609
## sex 0.74 0.43 0.274
## sex:target 0.32 0.07 0.163
## block:sex 0.32 0.21 0.578
## block:sex:target 0.05 7.12e-04 0.013
##
## * Compared among: all models
## * Priors odds: uniform-equalQuadrant 1L:
## Bayes factor analysis
## --------------
## [1] target + participant : 6417.72 ±0.56%
## [2] block + participant : 39.14886 ±1.28%
## [3] target + block + participant : 420371.6 ±0.92%
## [4] target + block + target:block + participant : 336219.6 ±1.25%
## [5] sex + participant : 0.239027 ±1.23%
## [6] target + sex + participant : 1600.186 ±2.16%
## [7] block + sex + participant : 9.627649 ±1.63%
## [8] target + block + sex + participant : 108616.4 ±4.74%
## [9] target + block + target:block + sex + participant : 83157.72 ±1.51%
## [10] target + sex + target:sex + participant : 160.3197 ±2.2%
## [11] target + block + sex + target:sex + participant : 10617.35 ±2.25%
## [12] target + block + target:block + sex + target:sex + participant : 8975.743 ±3.94%
## [13] block + sex + block:sex + participant : 2.209176 ±1.64%
## [14] target + block + sex + block:sex + participant : 27460.6 ±3.8%
## [15] target + block + target:block + sex + block:sex + participant : 21790.32 ±1.73%
## [16] target + block + sex + target:sex + block:sex + participant : 2705.391 ±2.52%
## [17] target + block + target:block + sex + target:sex + block:sex + participant : 2242.611 ±4.72%
## [18] target + block + target:block + sex + target:sex + block:sex + target:block:sex + participant : 119.6571 ±7.54%
##
## Against denominator:
## pathlength ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 1.00 7.05e+03
## block 0.74 0.99 44.64
## block:target 0.32 0.44 1.70
## sex 0.74 0.26 0.125
## sex:target 0.32 0.02 0.053
## block:sex 0.32 0.05 0.121
## block:sex:target 0.05 1.16e-04 0.002
##
## * Compared among: all models
## * Priors odds: uniform-equalQuadrant 1W:
## Bayes factor analysis
## --------------
## [1] target + participant : 42.88525 ±0.69%
## [2] block + participant : 3.453571e+13 ±0.99%
## [3] target + block + participant : 6.512697e+15 ±1.35%
## [4] target + block + target:block + participant : 4.77764e+17 ±2.32%
## [5] sex + participant : 0.1829386 ±0.94%
## [6] target + sex + participant : 8.39136 ±3.42%
## [7] block + sex + participant : 7.009781e+12 ±5.24%
## [8] target + block + sex + participant : 1.283335e+15 ±1.85%
## [9] target + block + target:block + sex + participant : 9.057146e+16 ±2.58%
## [10] target + sex + target:sex + participant : 0.8117047 ±9.26%
## [11] target + block + sex + target:sex + participant : 1.304967e+14 ±2.86%
## [12] target + block + target:block + sex + target:sex + participant : 1.000667e+16 ±2.92%
## [13] block + sex + block:sex + participant : 449793218028 ±1.83%
## [14] target + block + sex + block:sex + participant : 9.252713e+13 ±4.85%
## [15] target + block + target:block + sex + block:sex + participant : 7.090916e+15 ±10.97%
## [16] target + block + sex + target:sex + block:sex + participant : 8.932372e+12 ±3.88%
## [17] target + block + target:block + sex + target:sex + block:sex + participant : 6.373164e+14 ±2.43%
## [18] target + block + target:block + sex + target:sex + block:sex + target:block:sex + participant : 1.14591e+14 ±2.37%
##
## Against denominator:
## pathlength ~ participant
## ---
## Bayes factor type: BFlinearModel, JZS
##
## Inclusion Bayes Factors (Model Averaged)
##
## P(prior) P(posterior) Inclusion BF
## participant 1.00 1.00
## target 0.74 1.00 5.05e+03
## block 0.74 1.00 3.98e+15
## block:target 0.32 0.99 157.38
## sex 0.74 0.19 0.081
## sex:target 0.32 0.02 0.040
## block:sex 0.32 0.01 0.029
## block:sex:target 0.05 1.93e-04 0.003
##
## * Compared among: all models
## * Priors odds: uniform-equalWe do not find any sex effects for path length.
Overall, in considering all analyses for device and sex comparisons, we find some differences but these are not consistent. These are likely due to the uneven sample sizes, where we have less mouse users and males in our data. Some of the differences we find involve mouse users overcompensating for the near target, and males having faster completion times than females. However, these differences were small and are likely not meaningful effects.